With only three dissenting votes, the Senate yesterday approved what would be the most radical overhaul of the federal income tax in more than 40 years, wiping out dozens of tax breaks, removing 6 million low-income Americans from the tax rolls and slashing tax rates for individuals and businesses.

The 97-to-3 vote virtually assures that President Reagan will achieve what he has said is the top domestic priority of his second term: a sweeping revision of tax law that will change the way the tax system affects the lives of virtually every American, a development few believed possible as recently as two months ago.

"The Senate has voted on tax reform and the score is: taxpayers 1, special interests, nothing," Reagan said in a written statement. "The Cinderella team came out on top." He told Senate leaders by telephone after the vote that he hopes to sign a tax-overhaul bill into law by Labor Day.

The legislation now goes to a House-Senate conference committee, which, starting in mid-July, is to iron out differences with a House version passed last December. While the bills vary on many particulars, both would eliminate many tax breaks, reduce rates dramatically, cut individual taxes at least $100 billion over five years and increase corporate taxes by the same amount.

Senate Finance Committee Chairman Bob Packwood (R-Ore.), who met yesterday with House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.), said: "We both agreed we're going to try to take the best we can out of both bills."

Calling both measures "better than present law," Rostenkowski said: "We approach the heart of reform from different angles. The challenge now is to take the best reforms from each and fuse them together."

Yesterday's vote marked a historic turn in the 73-year history of income tax legislation, in which Congress continually has bowed to interest groups, creating a plethora of deductions and credits while looking to high rates to recoup revenue.

In more than a year of congressional deliberations, the Tax Reform Act of 1986 faced death at least three times -- in the House Ways and Means Committee, on the House floor and eight weeks ago in the Senate Finance Committee -- as advocates of various tax breaks joined forces to overwhelm those seeking change.

But Packwood in late April unveiled a radical proposal, fashioned after a plan by Sen. Bill Bradley (D-N.J.), that would wipe out many deductions and drive rates so low that few senators dared oppose it.

"Each senator was willing to sacrifice something that was important to his or her state to do what was in the best interest of the country," said Bradley, whom Packwood yesterday dubbed "the godfather" of the Senate bill.

The proposal passed the Finance Committee and the Senate without substantial amendments -- an almost unheard-of occurrence attributed largely to a requirement that any tax breaks restored be coupled with tax increases, so that the bill would not increase the huge budget deficit.

These austere ground rules fractured every coalition that sought significant change, as opponents of higher taxes joined with those opposed to altering the bill to defeat one amendment after another.

"The most spectacular legislative miracle I have ever witnessed during the course of my years in the U.S. Senate," was the way Sen. Lowell P. Weicker Jr. (R-Conn.) described it.

The three nay votes yesterday came from Democratic Sens. Paul Simon (Ill.), John Melcher (Mont.) and Carl Levin (Mich.), who argued that the bill would heap too much tax relief on the wealthy and too little on the middle class.

In an interview on the "MacNeil/Lehrer NewsHour" last night, Rostenkowski said the Senate bill could not pass the House in its present form. He named three trouble spots: Senate limits on deductions for Individual Retirement Accounts, its limits on state sales taxes and the relative amount of tax relief for the middle class.

The Senate bill would almost halve the top individual tax rate of 50 percent, replacing the 15 existing tax brackets with two -- 15 percent and 27 percent. It would almost double the personal exemption to $2,000 and raise the standard deduction to $5,000 on joint returns, thereby removing 6 million low-income Americans from the tax rolls.

For corporations, the top rate would drop by almost one-third, from 46 to 33 percent.

In exchange for the low rates, the bill would impose stern tradeoffs.

On the business side, it would repeal the investment tax credit, a $38 billion-a-year subsidy for equipment purchases; close an array of tax advantages for real estate development; trim writeoffs for the so-called "three-martini lunch," and impose a stiff minimum tax limiting the value of deductions for everything from equipment depreciation to the growing of trees.

Among the changes for individuals, the bill would wipe out most tax shelters, repeal the low rate for capital gains and disallow deductions for contributions to Individual Retirement Accounts by those covered by company pensions, while still deferring taxes on interest earned on IRAs.

It also would repeal deductions for most sales taxes and for consumer interest, such as on car loans and credit cards, and would significantly cut deductions for medical and work-related expenses.

The bill aims to treat taxpayers with the same incomes similarly rather than favoring certain people and activities over others, the situation under the present system. About 80 percent of individual taxpayers would fall in the 15 percent bracket.

Within those broad outlines, however, lurk vestiges of the existing system. The bill would retain certain entrenched breaks for defense contractors, banks, oil, timber, steel, insurers and many more -- although some of these would be devalued by the minimum tax.

It also would retain the home mortgage deduction, a $30 billion-a-year subsidy for homeowners, and allow taxpayers who itemize deductions to write off charitable contributions while denying that benefit to nonitemizers.

Although the official, top rate for individuals is 27 percent, the actual marginal rate for two-earner families making $75,000 to $145,000 a year (and for single taxpayers making $45,000 to $127,000) is higher because the bill would phase out certain tax advantages as income increases. For example, a family of four making $75,000 would effectively face a 32 percent bracket.

Moreover, while taxpayers would experience a 6.4 percent average tax cut, congressional calculations show that tens of millions of middle-income people would pay more taxes -- and many more in the $20,000 to $40,000 range would enjoy very small tax cuts -- because their rate cuts would not compensate for the loss of deductions.

Still more people would experience tax increases during 1987, the first year that the bill would take effect, because loopholes would be closed on Jan. 1, while rates would not be cut until July 1.

"Most of us concur we need to find a way to move that rate cut up to Jan. 1, 1987," said Sen. Lloyd Bentsen (D-Tex.), a senior Finance Committee member who is all but certain to be named to the House-Senate conference committee.

Senate Majority Leader Robert J. Dole (R-Kan.), another certain conferee, agreed with Bentsen, saying he also will press in the House-Senate panel to do away with the bill's higher-than-advertised tax rates and to allow a longer transition period before wiping out most tax shelters.

The Senate vote follows a long and elusive quest for fairness in U.S. taxation as the tax burden on the poor has increased while deductions and tax shelters have proliferated.

The bill that emerged yesterday represented a rare convergence of forces -- a Republican president bent on cutting taxes, a nascent congressional tax-overhaul movement backed by presidential contenders in both parties and unprecedented public outcry over legalized tax avoidance by the rich and profitable corporations.

The House passed a tax-overhaul package last December, only days after Republicans seemed to have killed it by voting en masse to block consideration of the package. After a rare pilgrimage to Capitol Hill by Reagan, the GOP forces voted to send the bill to the Senate along with a plea for more favorable treatment for business.

Packwood, who a year earlier had said he liked the tax code "the way it is," at first tried drafting a bill preserving most deductions cherished by his committee. Within weeks, the measure was threatening to increase the deficit by $100 billion over five years.

"This bill was dead as a dodo bird two months ago," Dole said. "He Packwood brought it back to life. He got the attention not only of the Finance Committee but of the American people."

Packwood pulled the bill off the table and one week later unveiled his radical proposal, declaring that he had been "converted" to Bradley's philosophy of low tax rates and fewer loopholes.

"How did we ever get people to move across the country from Missouri along the Oregon Trail to Oregon and California to farm," Packwood asked in the opening day of Senate debate, "because when they got there, there was no investment tax credit and there was no capital gains and there was no income averaging because there was no income tax?"

In the Finance Committee, Packwood assembled a core group of three other Republicans and three Democrats, making political concessions to each in return for a commitment to oppose all changes in the package. Together they steered the bill through the committee by a vote of 20-to-0.

For 13 days of debate on the Senate floor, Packwood took charge of lining up Republican votes and Bradley lined up Democrats. Deputy Treasury Secretary Richard G. Darman, a chief administration strategist on the issue, said the package forced senators to vote for or against tax overhaul rather than focusing debate on particular tax breaks.

In the hours before yesterday's final vote, most of the 40-some amendments remaining on the schedule were withdrawn or not offered. Only one major amendment was approved: Senators agreed 50-to-47 to a nonbinding resolution urging Congress not to change the tax code again for five years.