But about 7,000 absentee ballots still need to be counted. The Alaska Elections Division said it would start counting the first of the absentee ballots Tuesday, Aug. 31. State law allows for up to 15 days to review and count absentee and questioned ballots.
Murkowski would have to win 60 percent of the absentee vote to take the lead.
Candidates can request a recount within five days of the results being certified, but they must pay for it from their own checkbook.
Miller and his supporters were jubilant in what most pollsters predict will be a win for him -- Sarah Palin dubbed it a "miracle on ice" in a Twitter posting. The candidate, a self-described "constitutional conservative," said in a statement that he was "very pleased" by the results and "we intend to work just as hard to communicate our message to the people of Alaska" in the general election.
But Murkowski, who is seeking a second term in office, isn't giving up yet.
"We know for a fact that it ain't over yet until it's over," she said at a press conference Wednesday. "There is much, much yet to be counted."
Miller trailed far behind Murkowski in funding -- the incumbent senator had raised nearly $3 million for her campaign as of Aug. 4, according to the Federal Election Commission, compared with $283,473 raised by Miller.
But it didn't take long for the tide to shift.
Sen. Lisa Murkowski Trails Behind Joe Miller
Miller gained momentum in the last two weeks, funneled by support from the California-based Tea Party Express and behind-the-scenes push from Palin.
"It was a David and Goliath kind of thing. I don't think anyone gave the possibility of Joe Miller winning much credibility until the last couple of days," said Alaska pollster Ivan Moore. "It's a huge surprise and I think Lisa got caught napping."
Some Republican insiders blamed Murkowski's apparent loss on her not taking Miller's threat seriously enough. One Republican strategist said that Murkowski's campaign was advised 10 weeks ago to use her huge bankroll to attack Miller.
Instead, she targeted President Obama and touted her work in helping Alaskans. It was only on Aug. 23 -- a day before the elections -- that she finally went up with a negative radio ad against Miller. At that point, it was too late.
"Lisa made a fatal error," GOP pollster and political consultant Marc Hellenthal said. "She was attacked with negatives and she ran her ads against Obama, who wasn't on the ballot.
"She didn't bother to say to anybody that the negatives weren't true. She blew a phenomenal lead, a 40-point lead."
If he wins the primary, Miller will face Sitka Gov. Scott McAdams in the general election in November. McAdams is a virtual unknown in the national political scene, so much so that even the Democratic National Committee spokesman couldn't recall his name Wednesday on "Top Line."
"His name is not Lisa Murkowski," DNC's Brad Woodhouse said when asked by ABC News' Jonathan Karl what the candidate's name is.