The nation's economy grew slightly in the third quarter instead of declining as reported earlier, the Commerce Department said yesterday, because businesses added more goods to their inventories than had been estimated.

The report that output was higher last quarter only added to worries that the recession will continue to deepen since businesses at some point will have to cut production to get inventories back into line with sales, which are falling.

The department now estimates that after adjustment for inflation the gross national product rose at a seasonally adjusted annual rate of 0.6 percent last quarter rather than falling at that rate as indicated by preliminary figures. At the same time, it also raised its estimate of inflation for the three months, as measured by the GNP deflator, from a 9.4 percent rate to 9 1/2 percent.

Corporate profits from current production rose $900 million in the quarter to an annual rate of $191.2 billion, the department reported.

Meanwhile, the rapid decline of interest rates continued as Continental Illinois Bank and Trust Co., the country's seventh-largest commercial bank, lowered its prime lending rate to 16 percent from 16 1/2 percent. Crocker National Bank of San Francisco had cut its rate to 16 percent earlier this week. Other major banks remained at 16 1/2 percent.

The GNP revision "does not change anything about the outlook," said economist Otto Eckstein, head of Data Resources Inc., a private forecasting firm. The economy will still decline at a 4 percent or 5 percent rate this quarter, he predicted.

Eckstein said the news his firm is getting from industry includes "universal reports of slashes in their 1982 capital programs, attempts, sometimes difficult, to get rid of inventory, reductions in employment, discounts and other prices cuts--every sign of recession."

That view is echoed by the majority of private economists and by those in the Reagan administration. There is more disagreement about when the recession will hit bottom, but most forecasters expect it sometime in the spring.

In current dollars, GNP rose to an annual rate of $2,956.6 billion. After adjustment for inflation, final sales in the third quarter fell at a 0.2 percent rate compared to a 4.7 percent rate of decline in the second quarter, when total real output dropped at a 1.6 percent rate. The difference between total output, or GNP, and final sales is the change in business inventories.

During both quarters, business was adding to its stocks at nearly a $25 billion annual clip while sales were falling. Indications are that sales are dropping even more rapidly now and that business is still adding involuntarily to its inventories. At some point, current production will be lowered not only to bring it in line with sales but even further, in order to reduce the level of stocks.

Such production cuts will mean higher unemployment. Yesterday, for instance, the Labor Department said initial claims for regular state unemployment benefits on a seasonally adjusted basis were at the 551,000 level for the week ended Nov. 11, the second consecutive week initial claims were that high. In August, when the unemployment rate was 7.2 percent, initial claims were running about 420,000 a week. The October unemployment rate was 8 percent.

Robert Ortner, chief economist at Commerce, said the upward revision in GNP is not encouraging because of the higher level of inventories. "This way, it looks like we have more recession ahead of us," he said.

Commerce Secretary Malcolm Baldrige noted that the Economic Recovery Tax Act of 1981 reduced corporate tax liabilities in the third quarter at an annual rate of $5.7 billion, or about 7 percent of total corporate tax bill. Nevertheless, Baldrige expressed concern that corporate profits as a share of national income fell to a level of 8.1 percent, compared to an average of over 10 percent in the late 1970s.