With Johnson all but guaranteed to be one of the two finalists, Hunt, Gove and Javid are battling for the second spot in the runoff.
The winner, expected to be announced in late July, will replace Theresa May as party leader and prime minister.
May stepped down as Conservative leader earlier this month after failing to secure Parliament's approval for her Brexit deal.
Today's vote ended the gravity-defying campaign of Stewart, who began as a longshot but sent an electric charge through the race as the "anti-Boris" candidate. He got just 27 votes, fewer than in the second round.
A former diplomat who once walked across Afghanistan and was a deputy provincial governor in Iraq after the 2003 US-led invasion, the 46-year-old MP called out his rivals for what he saw as their fantasies and empty promises, and called for compromise on Brexit.
His quirky campaign, which saw him crisscross Britain talking and listening to voters, struck a chord with the public — though was less of a hit with his Conservative colleagues in Parliament.
After the result, Stewart said it had been "the most incredibly wonderful, exciting campaign."
He said that although he had not managed to persuade his colleagues, the public reaction proved that "pragmatism" and "the centre ground" were alive and kicking in politics.
Hunt, who got 54 votes, and Gove with 51 are tussling for second place and the slot of Johnsons' runoff opponent. Javid straggled in fourth place, with 38 votes.
Many in the party doubt that anyone can beat Johnson, a quick-witted, Latin-spouting extrovert admired for his ability to connect with voters, but mistrusted for his erratic performance, and record of inaccurate and sometimes offensive comments.
Hunt is considered an experienced and competent minister, but unexciting. Javid, the son of Pakistani immigrants, says he offers a common-man alternative to his private school-educated rivals like Johnson and Hunt, although he was a highly paid investment banker before entering politics.
Gove is the sharpest performer and could come out best in head-to-head debates with Johnson, his longstanding frenemy.
Like Johnson, Gove helped lead the campaign to leave the European Union, but scuttled his friend's bid to become prime minister in 2016 when he unexpectedly withdrew his support and decided to run for the job himself. The move left him with a lingering taint of treachery in the eyes of some Conservatives.
All the candidates to replace May have vowed to succeed where she failed and lead the country out of the EU. They differ widely on how to do that — and critics say none of their plans is realistic.
The EU says it won't reopen the Brexit agreement it struck with May's government, which has been rejected three times by Britain's Parliament. Many economists and businesses warn that leaving without a deal on divorce terms and future relations would cause economic turmoil as tariffs and other disruptions are imposed on trade between Britain and the EU.
Johnson has won backing from the party's die-hard Brexiteers by insisting the UK must leave the bloc on the rescheduled date of October 31, with or without a divorce deal to smooth the way.
The UK's withdrawal, originally set for March 29, has been pushed back twice amid political deadlock in London.
Johnson said during the TV debatethat there would be a "catastrophic loss of confidence in politics" if Brexit was delayed any further.
Javid, like Johnson, says he would try to leave the EU without an agreement rather than delay Brexit beyond October 31. Gove and Hunt both say they would seek another postponement if needed to secure a deal, but only for a short time.
- AP
