Moving even faster than the Federal Reserve apparently wants, several of the nation's largest banks raised their prime lending rate yesterday from 14 1/2 percent to 15 percent, another record.

Morgan Guaranty Trust Co. of New York, the country's fifth largest bank, acted first. Other large banks in New York, Chicago and Philadelphia immediately followed suit.

Only two weeks ago, the prime rate, which banks charge their most credit-worthy corporate customers, rose from 13 1/2 percent to 14 1/2 percent after a series of Federal Reserve actions reducing credit availability in an attempt to curb inflation.

Now rates to most borrowers are rising. Mortgage rates at some California savings and loan associations, for example, are 14 percent, and in some parts of the country, mortgage money is becoming difficult to find at any price.

In other economic news yesterday, two more major oil companies announced big increases in their third-quarter profits. Gulf Oil Corp., fifth largest among the majors, said its net income rose 97 percent from the comparable quarter a year ago to $416 million. At Conoco Inc., the ninth largest, profits jumped 133 percent to $247.1 million.

On Monday, Exxon Corp., the oil giant, said its net income was up 118 percent in the third quarter to $1.14 billion, primarily because of earnings in other countries.

Treasury Secretary G. William Miller said the increases in oil company earnings "reinforce the urgent need for the Congress to enact promptly the administration's windfall profits tax." [Details on Page E1. ]

Also yesterday, the Commerce Department reported new orders for durable goods -- items such as factory machinery, airplanes and automobiles -- rose by 5.9 percent in September, the largest monthly increase since August 1978. The report was another sign of the continued strength in the economy that was one of the reasons the Federal Reserve decided to clamp down on credit.

Ever since the Fed moved Oct. 6, its chairman, Paul Volcker, has been urging bankers to "move no more rapidly than necessary" in raising interest rates on their loans.

But the Fed that day changed its previous method of trying to control the expansion of money and credit by mainly pegging certain interest rates. During the last two weeks as a result, many money market interest rates have swung wildly up and down as investors, bankers, borrowers and lenders generally have tried to learn how to play the new game.

Volcker has been trying to dissuade bankers from seizing upon temporary increases in their cost of acquiring funds to lend -- say, by issuing large certificates of deposit -- as an excuse for raising their lending rates.

"In a situation in which there could be greater day-to-day volatility in money market rates . . . pricing of your own loans seems to me more a matter of responsible business judgment than of following a rote formula, related solely to the cost of some small margin of loanable funds," Volcker told the annual meeting of the American Bankers Association on Oct 9.

Last week he passed the same message to an invited group of about 30 bankers from across the country in a meeting at the Federal Reserve headquarters here. Don't follow every last jiggle of the market, he urged.

A bank official at Morgan Guaranty declined to comment on its reasons for boosting the prime, saying only that several factors were involved, primarily the bank's cost of acquiring funds and the demand for business loans.

The Fed intervened this week in the markets, making more funds available to banks when a key interest rate, the so-called federal funds rate, was about 18 percent. Before Oct. 6, the Federal Reserve used that rate, which is charged by banks on overnight loans of reserves to each other, as virtually its sole guide on whether to add or subtract cash from the banking system.

Now the Fed apparently is willing to accept a very wide fluctuation in the federal funds rate, perhaps from about 12 percent to 17 percent, some analysts suggest.

Exactly what prime rate is consistent with those levels of the federal funds rate is very difficult to determine, analysts said. But Federal Reserve officials are anxious that bank lending rates go up more or less in line with their average cost of acquiring lendable funds, not just the swift upward movement of the most expensive of those funds.

Federal Reserve sources said this is partly based on fear of political repercussions in the months ahead when the Fed's new tighter policy really begins to bite. At that point, the sources said, the Fed would like to have built a record of urging moderation upon the banks in interest rate changes and of urging them to keep funds flowing to all types of borrowers.