The Senate Finance Committee yesterday voted unanimously to reverse the one major Social Security benefit cut that President Reagan was able to push through Congress last summer.

In a session whose stated purpose was to help shore up the Social Security system, which most Republicans believe will require future benefit cuts, the committee voted instead to restore the $122-a-month minimum benefit to all 3 million current beneficiaries except for retired federal, state and local government workers receiving government retirement benefits, and persons residing overseas. Special benefit provisions for nuns were also approved. Under the budget cuts voted last summer at the president's request, all 3 million would have seen their benefits cut next March.

To finance restoration of the minimum, the committee nibbled at two other existing benefits, sick pay and the family maximum.

To shore up the largest and weakest of the Social Security trust funds, out of which come old-age and survivor benefits, the committee also agreed to allocate to this some of the Social Security tax revenues now channeled into the better-off disability and health insurance funds, and to allow the old-age fund to borrow from the disability fund.

Chairman Robert J. Dole (R-Kan.) and Sen. Daniel Patrick Moynihan (D-N.Y.), who has argued that interfund borrowing guarantees system soundness for the short term, were all smiles as the roll was called on the four-part bill, with only Harry F. Byrd Jr. (Ind-Va.) unrecorded. Dole said its provisions may be added as an amendment to the debt limit bill on the floor, possibly today.

The committee action came as Reagan, in his address last night, also called for conditional restoration of the minimum to those now on the rolls, and backed part way off other Social Security benefit cut proposals he made earlier this year.

The president's proposal to cut off the minimum benefit had brought such an outcry that the House, in a ploy engineered by Democratic leaders, voted to restore it last summer at virtually the same time that the final legislation killing it was clearing Congress.

Democrats claim that most of the benefit cuts sought by the president earlier this year are not needed to keep Social Security solvent, and say Reagan really is out to use Social Security to help balance the budget.

Moynihan and other liberal Democrats argued that interfund borrowing and reallocation would probably keep the system sound for the 1980s and indicated their belief that large benefit cuts were designed to help Reagan balance the budget. William L. Armstrong (R-Colo.), Dole and other Republicans denied this, arguing that the system will go bankrupt without much more serious action than interfund borrowing.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) repeated yesterday that the only bill the House will take up this year would be one to authorize interfund transfers and restoration of minimum benefits.

In addition to interfund borrowing and reallocation, the bill would raise money to offset restoration of the minimum by making sick pay subject to the Social Security tax for the first six months of illness; and by limiting total benefits for a family in retirement and survivor cases to 150 percent of the basic payment due the retired worker instead of 188 percent, applicable only to those going on the rolls in the future.

The bill restores the minimum benefit only for those already on the rolls; persons retiring in the future will get only their earned amount, except for nuns, who could still qualify for the minimum if they retire in the next 10 years. About 350,000 federal, state and local employes currently getting the minimum will have it reduced to the extent that they have non-federal government pensions exceeding $300 a month but in no case below their actual earned Social Security entitlement.