With 10 of 10 precincts reporting, Alexander tallied 52 percent of the vote to Snelling's 48 percent, according to totals listed on the Georgia Secretary of State's web site.
Alexander, a Douglasville resident with strong ties to Paulding County, won 57 percent of the vote in the Douglas County part of the two-county district. Snelling, also of Douglasville, easily won in the heavily Republican Paulding County part of the district, but could not overcome the Douglas County vote.
She won by about 1,100 votes out of a total 22,000 votes cast in the election.
Snelling was seeking a return to the Georgia General Assembly after serving four terms before departing in 2002.
Alexander had lost previous races for Hiram City Council and Georgia House District 67.
In other legislative races, south Paulding resident Micah Gravley easily defeated Leigh McMutry of Winston for the House District 67 seat.
The seat was left vacant when Bill Hembree of Winston resigned to run for the vacant Senate District 30 seat.
Hembree won 48 percent of the vote in a special Republican primary for the seat today. He will face Mike Dugan of Carrollton in a Dec. 4 runoff after Dugan received 24 percent of the vote to finish second out of four candidates.