Foreign Minister Jeremy Hunt picked up 46 votes and environment minister Michael Gove 41. Interior minister Sajid Javidscraped through with exactly 33.
Britain is frantically searching for a leader after Prime Minister Theresa May stepped down last month as Conservative party chief over her repeated failure to deliver Brexit.
The island nation is now due to split away from the other 27 European Union member states on October 31.
Further rounds of voting scheduled for Wednesday and Thursday will whittle the list of contenders down to just two.
The finalists will face the ruling party’s 160,000 grassroots members in a vote next month to decide the winner.