Republican U.S. Sen. Saxby Chambliss faces Democrat Jim Martin after a monthlong sprint of post-general election campaigning that drew national political heavyweights from both parties. Polls opened in Georgia at 7 a.m. and were scheduled to close 12 hours later.
In Minnesota, a recount that could take weeks is under way in a tight race between Republican Sen. Norm Coleman and Democrat Al Franken.
Chambliss and Martin both fell short of the 50-percent threshold in a three-way general election race with Libertarian candidate Allen Buckley, who drew 3.4 percent of the vote. It's Georgia's first Senate runoff since 1992, when Democratic Sen. Wyche Fowler was upset by Republican Paul Coverdell.
Chambliss is seeking a second term after winning a longshot bid in 2002 against Democratic Sen. Max Cleland. That campaign infuriated Democrats with a TV ad that questioned Cleland's commitment to national security and flashed a photo of Osama bin Laden.
Martin has aligned himself with President-elect Barack Obama's message of change, and has vowed to provide economic relief for the middle class. Chambliss has played to his base by promising to be a firewall against a Democratic-dominated Washington getting a "blank check."
Voting was running smoothly Tuesday morning with no problems reported to state election officials as of 8 a.m., said Georgia Secretary of State spokesman Matt Carrothers.
Early voting statistics were encouraging for the Chambliss camp. Of the nearly 500,000 early voters who returned to the polls, turnout among black voters is down and turnout among white males is up compared with advance voting before the general election.
White males normally are a solid Republican constituency in Georgia, while exit polls showed that Martin won the votes of nine of ten Georgia blacks who registered a preference.
Still, analysts say it's hard to tell how that may impact Tuesday's contest.
"It doesn't mean the overall turnout will be skewed," said Emory University political scientist Alan Abramowitz. "It could just mean that there's much less incentive to early vote this time, because no one's expecting there to be long lines now."
Georgia Secretary of State Karen Handel did not predict turnout for the contest, but the 1992 runoff attracted about 1.2 million voters - roughly half the turnout in that year's general election.
Roughly 4 million people cast ballots in this year's general election, and both sides have since tried to keep voters' attention with a barrage of ads and visits by political heavy-hitters.
Former President Bill Clinton and former Vice President Al Gore both stumped for Martin. President-elect Barack Obama recorded a radio ad for Martin and sent the campaign 100 field operatives to boost turnout. But he didn't campaign in the state, despite a request from Martin to do so.
Several ex-Republican presidential candidates made appearances for Chambliss, including GOP nominee John McCain, former New York Mayor Rudy Giuliani, former Massachusetts Gov. Mitt Romney and former Arkansas Gov. Mike Huckabee.
Alaska Gov. Sarah Palin, McCain's vice presidential pick, held four raucous rallies for Chambliss that drew thousands of party faithful on the eve of the election.