President Carter got another round of good preelection news yesterday as the Commerce Department reported that the economy climbed out of its recession last quarter, that inflation eased slightly and that housing starts rose in September for the fourth consecutive month.

New government figures showed that the "real" gross national product -- the actual volume of goods and services the economy produces -- grew at a 1 percent annual rate between July and September, after plunging the previous quarter at a postwar record annual rate of 9.6 percent.

At the same time, however, several of the nation's leading banks -- disregarding Carter's warning that they may be jeopardizing the young recovery -- raised prime interest rates to 14 percent yesterday. [Details on Page D1].

The new figures on the economy provided another shot in the arm for Carter's campaign, which has been helped in recent weeks by improving statistics on unemployment and inflation. The reports are among the last to be issued before the Nov. 4 election.

Economists cautioned that the recovery could stall if interest rates, particularly home mortgage rates, continue much higher. And analysts say the inflation outlook is being clouded by the prospect of sharper increases in food prices.

In a further development that could worsen inflation, the Federal Reserve Board reported that the nation's basic money supply surged by a staggering $4.1 billion during the week that ended Oct. 8, overwhelming efforts by the Fed to rein in monetary growth.

The rise in "real" GNP last quarter, while generally in line with recent forecasts, marked an earlier-than-expected end to the 1980 recession. Most forecasters had thought the recession would linger through the first part of next year, and Carter administration officials had predicted as late as last July that the third-quarter figures would show a decline. The April-June plunge, while the steepest on postwar record, was the only quarter of actual decline.

Although economists sometimes say it takes two consecutive quarters of economic decline to make a recession, that is only a rule of thumb and not a formal definition. Whether a downturn is a recession is determined by the National Bureau of Economic Research, a private economic research center, which already has declared the 1980 slump a recession.

Courtenay M. Slater, the Commerce Department's chief economist, conceded the administration had underestimated the resiliency of the economy in preparing its earlier forecasts. She said consumers proved to be "not as fundamentally shaken as we thought" they would be.

Slater also backed away from President Carter's recent assertion that the recovery is being threatened by the recent rise in interest rates. She predicted interest rates were "likely now to level off and possibly ease down" and said the "threat . . . will not come to pass."

Yesterday's reports showed these developments:

"Real" GNP, or the economy's total output, adjusted for inflation, grew at a modest 1 percent annual rate during the third quarter of this year.

Inflation, as measured by the broad GNP index, slowed to a 9.1 percent annual rate during the period, compared with 10.7 percent the previous quarter. The portion of the index most closely affecting consumers rose at a 9.5 percent annual rate, down from 11.2 percent.

It was the first time since late 1978 that inflation on items purchased by consumers had fallen below a 10 percent annual rate.

Meanwhile, the department reported separately, that housing starts across the nation grew a robust 9 percent in September to a new annual rate of 1.544 million units, following a 12.7 percent rise in August and hefty increases in June and July.

The rebound in economic activity last quarter came almost entirely in final sales -- the broadest measure of overall buying -- indicating the bounceback was solid. Adjusted for inflation, final sales rose at a respectable 3.7 percent annual rate, after declining at a 10.2 percent pace from April to June.

Net exports also rose sharply during the quarter. And businesses continued to work off excess inventories, which should pave the way for a pickup in new orders and higher production levels later. Government purchases declined during the period.