The nation's economy may have grown at a moderate pace in the final quarter of last year rather than sliding into the recession most economists predicted, a top government economic official said yesterday.

Courtenay M. Slater, the Commerce Department's chief economist, said early -- and still very rough -- calculations show that "real" economic output may have risen at a 2 to 3 percent annual rate over the period.

Previously, economists had expected the actual volume of goods and services the economy produces to grow at only a 1.5 percent annual rate. The ecomony grew at a 3.1 percent annual pace in the third quarter of last year.

Meanwhile, President Carter's budget director, James T. McIntyre, speaking to business and civic leaders at The Washington Post's annual economic outlook luncheon, acknowledged yesterday that the nation is "going to have a major tax cut" sometime "in the next year or so," to offset inflation pushing taxpayers into higher brackets.

However, officials reiterated later that McIntyre merely was speaking abstractly and that Carter still is not planning to propose a tax cut in the budget he will send Congress later this month.

Carter and his advisers have concluded the economic outlook is too uncertain to justify proposing a tax cut at the time and that any premature action might worsen inflation.

The estimate disclosed by the Commerce Department's Slater was the highly preliminary "flash" figure compiled by the department each quarter using fragmentary data that is available before the public statistics are figured.

These estimates frequently are not reliable, although government anlysts watch them closely for a hint of what the more complete statistics may show. The department's formal estimate of real output is due a week from Friday.

The better-than-expected fourth quarter prformance would not change economists' forecasts that a recession still is likely in 1980. Analysts say the faster growth rate most likely stems from heavy Christmas sales.

Nevertheless, the news was enough to push stock prices up sharply late yesterday, adding to earlier gains posted as a result of the administration's actions in response to the Soviet invasion of Afghanistan.

Meanwhile, the Federal Reserve Board reported that consumers cut back their use of installment credit in November to the lowest level since last summer, possibly reflecting the start of a retrenchment move.

The board said extensions of new credit declined 4.4 percent over the month, perhaps in response to high interest rates. At the same time, borrowers also slowed their repayment of existing loans -- another sign of belttightening.