Armey was challenged by Dunn, Steve Largent of Oklahoma, a former Seattle Seahawks Hall of Fame receiver, and J. Dennis Hastert of Illinois.
On the second ballot, Armey received 99 votes, Largent received 73, and Dunn received 49. Hastert ran fourth on the first ballot and was dropped, following caucus rules.
Dunn was eliminated on the second ballot, and Armey and Largent went to a third ballot, which Armey won, 127-95.
As expected Wednesday, House Republicans endorsed Rep. Bob Livingston to succeed Newt Gingrich as speaker as the rattled GOP struggled to recover from an election that left it clinging to a 12-seat House majority.
Livingston, who chairs the House Appropriations Committee, was nominated by a voice vote in a closed-door meeting of the 223 House Republicans who will serve in the 106th Congress. With the backing of the majority party, the Louisiana lawmaker is assured election to the job when the new House convenes Jan. 6.
Livingston was unopposed in his bid to become leader of the chamber's Republicans and No. 2 in the constitutional line of succession to President Clinton, behind Vice President Al Gore.
Rep. Tom DeLay of Texas was unchallenged as majority whip, the No. 3 leadership job.
But No. 4 leader Rep. John Boehner of Ohio lost his conference-chairman job to Rep. J.C. Watts of Oklahoma. Watts, a conservative and former University of Oklahoma quarterback and professional football player in Canada, is the only black House Republican.
"I just want to say that once again this is a historic day for the Republican Party," Dunn said following the vote. "We've broken yet another glass ceiling. This is the first time ever a woman has run for a top leadership position, and I'll just tell you all the folks who have written me from all over the country, it's a great groundbreaking day for women. I'll be there to support the team in every way possible. We're going to win more elections."
Dunn said Tuesday she was 10 or 15 votes behind Armey heading into today's balloting for the majority leader job and hoped to win on a second ballot.
The Bellevue Republican said before the vote she had "a whole lot of second-ballot commitments" and could triumph after losing a first ballot to Armey.
Dunn had hoped to become the first woman majority leader by riding a wave of dissatisfaction with Armey, along with what she hoped were her colleagues' wishes for a proven communicator and diversified leadership team.
Political analyst Stuart Rothenberg said before the vote that some in the caucus may want to select a woman, but most would have differing reasons for their votes, ranging from who is the most conservative to who is the best inside player.
"It will come down to who individual members are comfortable with," he said.
The loss means Dunn will drop off the leadership team, since she had not sought re-election to her current leadership post as GOP vice chairwoman.