The economy grew at an unexpectedly sharp 4.3 percent annual rate from July through September, the strongest gain in nearly a year and a marked improvement over its sluggish performance in the first half of the year, the government said yesterday.

The Commerce Department earlier had reported that the gross national product -- the nation's total output of goods and services -- had increased at a 3.3 percent annual rate in the third quarter. But yesterday it revised that figure a full percentage point higher and credited strong automobile sales and production this summer and a sharp jump in defense spending.

The Reagan administration, which has predicted the economy would speed up from its 0.3 percent real growth rate in the first quarter of the year and 1.9 percent rate in the second, said yesterday the new GNP report vindicated its earlier forecast of a sharp rebound in the second half of the year.

"We're coming into the new year with some pretty good numbers," Council of Economic Advisers Chairman Beryl Sprinkel said. "It's solidly in the bag. It looks pretty good to me. We're certainly not on the verge of a sump hole of economic activity."

Sprinkel said the administration planned to stay with its forecast of 5 percent real growth for the last half of the year and 3 percent growth for the full year. He said fourth-quarter growth should be between 5 and 6 percent. With yesterday's revision, GNP would have to grow at a 5.7 percent rate in the last three months to achieve the administration's goal.

Many economists said they were surprised by yesterday's figures and had expected Commerce to revise downward its earlier estimate of 3.3 percent growth in GNP. With the upward revision, the third-quarter rate was the fastest since a 4.3 percent pace in the fourth quarter last year.

Despite the encouraging figures yesterday, many analysts said they doubted the economy would do more than continue to muddle along because a major force behind the stong growth in the third quarter was a sharp increase in automobile sales, spurred by cut-rate financing programs that have since ended.

However, David Jones, an economist with Aubrey G. Lanston, said the Big Three automobile companies -- General Motors, Ford and Chrysler -- plan to keep production high for cars in the next few months and reinstitute their successful automobile incentive programs this winter to improve their market share against other American and Japanese auto makers.

"The economy's on a firm foundation," Jones said. "I don't see any basis for any significant renewed strength, but it's on a firm foundation."

Some analysts also were pessimistic about future economic activity because business outlays have slowed and consumers, with historically high debt and low savings, aren't expected to maintain their rapid spending pace. Commerce said yesterday that personal saving as a percentage of disposable personal income dropped to a 35-year low of 2.7 percent from 5.1 percent in the second quarter.

Inflation and corporate profits both improved in the summer over the second quarter, Commerce said. Inflation, gauged by the fixed-weight deflator -- a measure of changes in prices -- slowed to a 3.1 percent rate in the third quarter, compared with 3.9 percent in the second, largely because of weakness in oil prices, Commerce said. Inflation ran at a 4.3 percent rate in the first three months of the year.

One drag on the economy continues to be trade, which economists say has diverted production from domestic businesses to foreign companies. During the third quarter, the U.S. trade picture continued to deteriorate, but not as badly as in the second quarter, Commerce said.

The trade picture "won't improve until next year," when the dollar declines further, allowing U.S. exports to become cheaper and imports relatively more expensive, said Paul Getman, economist with Chase Econometrics. "It's not likely we're going to see a big change until we see a big shift downward in the dollar. Growth is going to still be relatively sluggish."

Commerce said that both real final sales and inventory investment contributed to the increase in third-quarter GNP.

Consumer expenditures rose substantially in the second and third quarters, while business' fixed investment declined slightly in the third quarter after a substantial increase in the second.

Federal government purchases rose $11.6 billion in the third quarter, of which $5.6 billion was in defense, a category that had been relatively stable.

Final sales, less exports, increased 6.8 percent, or $28 billion, compared with an increase of 5.9 percent, or $24 billion, in the second quarter.