The Arlington County Board, splitting along party lines, approved yesterday a 1-cent increase in this year's real estate tax rate that nevertheless will mean the owner of an average $110,945 house will pay $20 less in property taxes this year because of decreasing property assessments.

The two board Democrats, John G. Milliken and Mary Margaret Whipple, and its Democrat-backed independent, Chairman Ellen M. Bozman, voted to increase the rate to 99 cents per $100 of assessed valuation, still the lowest rate in the metropolitan area.

"There's nothing an elected official likes better than lowering taxes, if you can do it without cutting services," said Bozman. The board plans to adopt a final budget April 23.

The board's two Republican-endorsed independents, Dorothy T. Grotos and Walter L. Frankland Jr., opposed the increase and pushed for a 95-cent rate. When that motion failed, the two lobbied unsuccessfully for a 97-cent rate and then the current 98-cent rate.

Grotos and Frankland, both of whom are up for reelection this fall, argued that the board had unnecessarily raised the tax rate 2 cents last year and pointed to the continually growing surplus for fiscal year 1984 that County Manager Larry J. Brown has been predicting in recent weeks.

Although that estimate stood at $2.2 million yesterday, Brown recommended a $1 rate, citing "major uncertainties" in federal and state revenues, and increased funding requests for schools, community activities and the Metro transit system above what he had included in his proposed $224 million budget.

"Some of those little bungalows have really been hit . . . ," said Grotos in arguing for a tax rate reduction. "For once, I'd like not to be so cautious and give the money back to the taxpayers this year." Yesterday's decision marked the second time in eight years that the property taxes of the average homeowner have declined.

The board's three majority members said they preferred to be cautious because of uncertainty about future property assessments, fee increases and the impact of a $5 million jury verdict against Arlington that the county plans to appeal.