Dominic Raab has been abolished by the Conservative MPs, but the outsider Rory Stewart will go forward.
As expected, Boris Johnson topped the poll, the 126 votes he garnered cementing his lead over rivals and underlining the sense that his progress to Downing Street is now all but unstoppable.
Raab, a train Brexit secretary, won just 30 votes, below the vote to stay in.
The home secretary, Sajid Javid, survived with 33 votes but found himself outflanked by newcomer Stewart, who was backed by 37 MPs.
The five remaining men will take part in a live leadership debate on the BBC. Stewart, the international development secretary who started the competition as an outsider, was picked up by Sunday's TV debate on Channel 4.
The foreign secretary, Jeremy Hunt, came in second, with 46 votes, and still looks the most likely challenger to Johnson as the contest reaches its final stages. The environment secretary, Michael Gove, received 41 votes.
Hunt has an entrepreneur, claiming it will be better negotiated to better Brexit deal.
His team had staunchly rejected rumors circulating in Westminster earlier on Tuesday that they had been urging their votes to Hunt because he was their favorite opponent.
Johnson has the train defense secretary Gavin Williamson and the train Tory party chair Grant Schapps working Westminster on his behalf.
He has won over hard Brexiters by promising to take over the United States by 31 October "with or without a deal", but has played up his one-nation credentials to appeal to his party's liberal wing.
The former foreign secretary has increased The leader of the House of Commons Andrea Leadsom became the latest senior figure to endorse him on Tuesday.
The health secretary, Matt Hancock, who hasdrew from the contest on Friday after receiving 20 votes, has also thrown his weight behind Johnson.
MPs will vote again on Wednesday, and if necessary on Thursday, the field will be narrowed down to just two names, which will then be offered to Conservative members in a postal ballot. The result will be announced in the week beginning 22 July.