WASHINGTON--The biggest surge in U.S. exports in six years helped to narrow the nation's trade deficit to $13.6 billion in March from $15.1 billion in February, the Commerce Department reported yesterday.

Although tempered by a rise in imports to record levels, the report was hailed by many economists as a sign that declines in the value of the U.S. dollar are finally beginning to pay off in easing the trade imbalance.

"We're into at least a slow turnaround. For sure, we've passed the worst," said Allen Sinai, chief economist for Shearson Lehman Brothers.

Exports increased by 12.9 percent in March, to $21.1 billion--the highest level since March 1981, when they were a record $22.9 billion.

Sales of U.S.-made manufactured goods overseas accounted for 80 percent of the increase in exports, with a $300 million rise in the sales of American computers and other office equipment leading the way.

Imports also increased in March, but at a much slower clip--up 2.9 percent to $34.7 billion. Still, that was enough to bring imports to a record level, surpassing the $34.3 billion mark set last October.

Analysts suggested, however, that the rise in imports was far less meaningful statistically than the rise in exports--up more than 20 percent so far this year.

Although the total amount spent on imports was higher, reflecting recent increases in the price of many foreign goods, the volume of imports coming into the country appeared to be leveling off.

"These figures are even better than they look. The substantial expansion of exports indicates the devaluation of the dollar is beginning to reverse the export stagnation of the last several years," said Jerry Jasinowski, chief economist for the National Association of Manufacturers.

At the White House, presidential spokesman Marlin Fitzwater said: "The trade figures indicate that the nominal trade deficit is gradually declining. Good news on the trade front."

For the first three months of this year, Americans have imported $40.9 billion more in merchandise than they have exported, suggesting an annual deficit $163.6 billion--compared with the record $166.3 billion deficit for all of 1986.

The value of the dollar has fallen nearly 50 percent against other major currencies over the past few years.

While President Reagan recently joined other industrial nation leaders in asserting that the dollar has fallen enough, this drop is expected to ease the trade deficit by making foreign goods more expensive at home and U.S. goods cheaper overseas.

However, improvement has been slow, partly because until recently foreign manufacturers have been reluctant to raise their prices for fear of losing their share of U.S. markets.

"The trade deficit is starting to move in the right direction," said Lawrence Chimerine, president of Wharton Economics. "But most people forget that adjustments bringing this about have a negative side effect: a weaker dollar, wage cuts, a squeezing of purchasing power and a pushing up of interest rates."

The U.S. trade deficit shrank against Japan in March, to $4.9 billion from $5.1 billion in the previous month.

However, the deficit with Japan, which reached $58.6 billion last year, remained this nation's largest. The trade gap with Canada also narrowed in March, to $1.5 billion from $1.9 billion in February.

But the trade deficit with Western Europe rose in the same period, to $2.5 billion from $1.9 billion in February, including a $1.6 billion trading shortfall with West Germany, the largest trade gap ever with that nation.

Commerce Department analysts cautioned against reading too much into the improvement between February and March, noting that many imports counted in February were actually received in January--suggesting that February's $15.1 billion deficit may have been over-stated and January's $12.3 billion deficit understated.

March's $13.6 billion deficit was thus only slightly down against the average $13.7 billion deficit for the first two months of the year.