As if taking a cue from a weekend of upsets in world tennis, Malcolm Turnbull, a former investment banker and lawyer, became the prime minister of Australia on Monday night after defeating incumbent Tony Abbott in a vote of Liberal Party lawmakers.

The vote was the second challenge to Mr. Abbott’s leadership in seven months. He won the government in September 2013.

Mr. Turnbull is a moderate Liberal, whose views, most recently on the legitimacy of same-sex marriage, had conflicted with those of his prime minister. The Liberals, despite their name, are the more conservative of Australia’s two major parties.

Mr. Turnbull won the support of 54 of his party colleagues, against 44 who voted in favor of Mr. Abbott’s retaining the party leadership.

Foreign Minister Julie Bishop will remain deputy leader of the Liberal Party. Ms. Bishop secured 70 votes, against 30 votes for her cabinet colleague Kevin Andrews. One lawmaker missed the vote for the leadership position, joining the session in time for the vote for deputy leader.

Mr. Turnbull called on Mr. Abbott to convene Monday night’s voting session earlier in the day. He resigned his position as communications minister and said at a news conference at Parliament House in Canberra, Australia’s capital, that he would challenge the prime minister for leadership of the Liberal Party.

“It is clear enough that the government is not successful in providing the economic leadership that we need,” Mr. Turnbull said at the news conference.

“It is not the fault of individual ministers,” he said. “Ultimately the prime minister has not been capable of providing the economic leadership our nation needs. He has not been capable of providing the economic confidence that business needs.”

At a separate news conference, Mr. Abbott agreed to hold the vote in Canberra on Monday night.

“The prime ministership of this country is not a prize or a plaything to be demanded,” Mr. Abbott said. “It should be something which is earned by a vote of the Australian people.

“There will be a party room ballot for both the leadership and deputy leadership position later this evening. I will be a candidate, and I expect to win.”

The previous Australian government, led by the Labor Party, lost an election in September 2013 after twice dumping its leaders. Kevin Rudd was elected prime minister in 2007, only to be replaced by his own party with Julia Gillard, Australia’s first female prime minister, in 2010. Ms. Gillard was replaced by Mr. Rudd in June 2013 just months ahead of the election.

Mr. Abbott said on Monday that he was dismayed at the attempt to destabilize his leadership from within his own party. But he had faced opposition from some party members over his conservative stances on same-sex marriage, climate change and pollution targets.

Mr. Turnbull entered Parliament in 2004. He was briefly leader of the Liberal Party, from September 2008 to December 2009, when the party was in opposition. He also holds more moderate views on climate change than Mr. Abbott and was deposed as leader.

Mr. Turnbull did not put himself forward as head of the Liberals when Mr. Abbott was challenged in February. At that time, the party voted 61 to 39 against a “spill motion,” which would have declared the party’s leadership and deputy positions vacant.