A sharply divided Arlington County Board voted yesterday to raise the county's real estate tax rate by 2 cents--the first increase since Republicans seized control of the board in the 1978 elections.

The tax rise, approved by a 3-2 margin with the board's Republican chairman joining two Democratic members, will bring the rate for residential and commercial real estate to 98 cents for each $100 of assessed value. Last year's rate was 96 cents. Arlington's property taxes are due in semiannual payments, May 15 and Oct. 15.

With real estate values increasing, the average assessment of a single-family Arlington home has climbed 5.5 percent since last year to about $110,000, county officials estimate. At the newly approved rate, the yearly tax on an average home would amount to $1,078--$22 more than the tax would have been at last year's rate.

Faced with a budget squeeze, the board's three-member Republican majority departed from goals set during the 1978 elections. The GOP members previously sought to reduce the real estate tax rate to offset rises in real estate assessments. The tax rate dropped steadily from $1.45 for each $100 of assessment in 1978 to $1.29 in 1979, $1.12 in 1980 and 96 cents last year.

To continue this strategy, the board would have had to reduce the rate to 91 cents this year, according to county officials. Such a move, however, appeared likely to require severe cuts in county programs, already facing tight budgets because of the current economic slowdown and the Reagan administration's reductions in federal aid.

Instead, two Republicans, Dorothy T. Grotos and Walter L. Frankland Jr., proposed to hold the line at 96 cents. Democrats Ellen M. Bozman and John G. Milliken recommended the 2-cent increase to 98 cents. Republican Chairman Stephen H. Detwiler, who must seek reelection in November, urged a 1-cent rise to 97 cents. "I don't want to support a tax increase," Detwiler said. But he argued, "If we go with 96 cents, I don't think we're going to make it."

During a sharp two-hour debate, all three proposals were initially voted down. At the end, however, Detwiler switched and backed the 2-cent rise. "I had to go one way rather than the other," he said later, contending that the 96-cent rate would provide insufficient revenue for contingencies. If the county's fiscal outlook improves, Detwiler added, he will propose a midyear tax cut.

The 2-cent increase will yield about $2.2 million in additional county revenue in the coming fiscal year, Arlington officials estimate. Combined with rising real estate assessments and a proposed $16.32-a-year increase in trash collection fees, the higher tax rate is expected to permit the county to meet the school board's request for $48.5 million. Nevertheless, county officials, who are seeking to complete action on next year's budget by April 24, say some programs still face substantial trims.