The nation's gross national product shot upward at a seasonally adjusted annual rate of 8.4 percent in the first quarter of this year, not 6 1/2 percent as first estimated, the Commerce Department said yesterday.

The revised figure for GNP showed the largest quarterly rate of increase in the output of goods and services since the second quarter of 1978, when it rose at a 9 percent clip. All of these estimates are adjusted for inflation.

Including inflation, GNP rose at a 19.3 percent annual rate in the first quarter to a level of $2.8538 trillion, the department said. The GNP deflator, which is the economy's broadest measure of inflation, rose at 10 percent annual rate in the fourth quarter, when real output increased at a 3.8 percent rate.

In the first such estimate for the quarter, the department said corporate profits from current production increased $19.3 billion to an annual rate of $202.6 billion compared with a $5.4 billion rise in the fourth quarter of 1980. After-tax profits climbed $4 billion to an annual rate of $168.3 billion.

The usually strong economic growth trend indicated by the revised GNP numbers is somewhat misleading, in the opinion of many economists. Most of the expansion actually occurred during the later part of the preceding quarter and in January, a fact masked by the usual comparison of quarterly averages for output. Since January, the economy apparently has grown only slightly, according to statistics on personal income, industrial production, retail sales and so forth.

Echoing this line, Commerce Secretary Malcolm Baldridge said the upward revision "does not alter our expectations for sluggish economic performance this quarter and next.

"Interest rates -- both short-term and long-term -- have rebounded," Baldride continued. "There has been no real increase in consumer spending since January, and total new construction has declined and will probably decline further. Gains in personal income have been very small, and the saving rate remains low."

Meanwhile, San Francisco's Bank of America, the country's largest, and number eight, Bankers Trust Co. of New York, followed the lead of other major banks yesterday and raised their prime lending rates to 20 percent. A number of analysts, however, think that could be the peak.

One of them, David Jones, an economist at the Wall Street firm of Aubrey G. Lanston & Co., called the increase a "delayed response" to April's sharp rises in other interest rates. "It looks like we could stabilize here, at least for a while," Jones said.

Most of the upward revision in GNP was concentrated in the nation's trade accounts and the figures for business inventories. Inventory investment by business was revised upward by $10.5 billion. Exports were found to be $5.3 billion higher than previously estimated, while imports were put at $7.4 billion less. Higher exports and lower imports both served to raise the GNP estimate.

The size of the revision surprised some economists. "It's a very startling large number," said Otto Eckstein, head of a private forecasting firm, Data Resources Inc.

"Maybe as much as a quarter of it was the weather," he said. "We had an exceptionally favorable winter for shopping in the North that helped retail sales.

"That's simply good luck," he added. Modest energy consumption and a sharp drop in oil imports also helped the overall picture, he said.