Ted Stevens was convicted on corruption charges last month
Alaska's Republican Senator Ted Stevens has lost his bid for a seventh term in office after a knife-edge race against Anchorage Mayor Mark Begich.
The Democratic candidate led the Senate's longest-serving Republican by 3,724 after Tuesday's count, with only 2,500 overseas votes to be tallied.
If the Democrats win two more Senate seats they would be able to prevent the Republicans from blocking legislation.
Minnesota's vote is due to be recounted while Georgia will hold a run-off vote.
The result means the balance of power in the Senate now favours the Democrats, says the BBC's Jonathan Beale in Washington.
With 58 of the 100 seats, they are now just two short of the 60 needed to overcome filibusters - a tactic used by the Senate minority to prevent legislation from coming to a vote.
Mr Stevens, 85, was seen almost as an institution in his state, our correspondent says, to the extent that the airport in Anchorage was named after him.
But the Senate race in Alaska was plunged into controversy when Mr Stevens was convicted last month of lying about gifts he had received from an oil company.
REMAINING SENATE RACES
Minnesota: Manual recount set to begin
Georgia: Run-off scheduled for 2 December
His defeat means the Senate will have its first Democratic representative from Alaska for 30 years.
In Minnesota, Democrat Al Franken, a well-known comedian, trails incumbent Republican Norm Coleman by just 206 votes, or 0.007% of the vote.
According to Minnesota state law, a winning margin of less than 0.5% of the vote triggers an automatic manual recount. The decision is expected to be taken on Tuesday, with the recount starting on Wednesday.
When ballots are counted by hand, candidates can often pick up votes, because human counters register votes that counting machines ignore.
In Georgia, because no candidate won more than 50% of the vote, a run-off between the top two candidates was automatically triggered.
Incumbent Republican Saxby Chambliss faces Democratic challenger Jim Martin in the 2 December vote.
A recent opinion poll from Research 2000 gave Mr Chambliss a three-point lead, with 49% to Mr Martin's 46%.
Former president Bill Clinton is due to campaign for Mr Martin on Wednesday.
As well as the three outstanding Senate races, the outcome of one state's presidential vote has still not been declared.
In Missouri, Republican John McCain is leading by some 4,900 votes, with only provisional ballots left to be counted.
LATE STATE RESULTS
Missouri: John McCain favoured to win
Nebraska: State officials announced on Friday that the vote was split for the first time ever
Provisional ballots are votes cast by people whose eligibility to vote is unclear on election day.
Even if all of the provisional ballots were declared valid, Barack Obama would have to win the vast majority of them to take the state.
So far, only one US network - NBC - has declared Mr McCain the winner in Missouri.
Last Friday, Nebraska officials declared that President-elect Barack Obama had won one of the state's electoral college votes.
It is the first time in recent US history that a state has split its electoral college votes.
Nebraska grants two electoral college votes to the winner of the state-wide vote, and one electoral vote for the winner in each congressional district.