By Rachel Kapochunas, CQ Staff

Democrat Mark Begich claimed victory Tuesday over Republican Sen. Ted Stevens , whose decades of dominance in Alaska politics were unraveled by a corruption conviction just a week before Election Day.

Begich’s success will give the surging Democrats effective control of at least 58 Senate seats in the upcoming 111th Congress.

It also will end the political career of Stevens, an aggressive champion of his state who was first appointed to the Senate in December 1968 and became the chamber’s longest-serving Republican. Tuesday was his 85th birthday.

Tuesday’s tally of thousands of remaining absentee ballots showed Begich extending his once-narrow lead to 3,724 votes, a margin of more than 1 percentage point. That prompted the Associated Press to declare Begich the victor late Tuesday afternoon Alaska time, a verdict echoed shortly thereafter by the Anchorage Daily News, the state’s biggest newspaper.

The Alaska Democratic Party said 2,500 overseas ballots remained outstanding at the close of counting Tuesday.

But Begich’s lead appears insurmountable. He had 150,728 votes, or 47.76 percent, versus 147,004 votes, or 46.58 percent for Stevens, out of 307,587 votes recorded.

Stevens — whose initial lead in the Election Night vote count was reversed during the count of absentee, early and provisional ballots — did not immediately make a statement following Tuesday’s developments. But in a release Begich said, “I am humbled and honored to serve Alaska in the United States Senate.”

“It’s been an incredible journey getting to this point, and I appreciate the support and commitment of the thousands of Alaskans who have brought us to this day,” Begich said.

Begich’s election will give at least a seven-seat gain to the Democrats, who entered the Nov. 4 elections with control of 51 seats including two held by independents who caucus with the party for organizational purposes. Two Senate races for Republican-held seats, in Georgia and Minnesota, remain undecided — keeping alive the Democrats’ hopes for reaching 60 seats, often called a “filibuster-proof” majority because a three-fifths vote is needed to end delaying tactics and proceed on Senate legislation.

Tuesday’s Count

Alaska elections officials on Tuesday resumed counting ballots that had been mailed in by Election Day or set aside because of questions during the initial count.

Wednesday is the deadline for all outstanding ballots to be counted. The target date for certification is Nov. 25, but officials say certification may not happen until the week after that.

Automatic recounts are only triggered by tie votes, under Alaska election law. If the margin is less than .5 percent, 10 qualified voters or the defeated candidate can request a recount at a cost to the state. If the margin is larger, the candidate requesting the recount must cover its cost. As the vote-counting ended Tuesday, Begich’s margin was 1.2 percentage points.