The former chancellor cemented his position as the favourite to succeed Boris Johnson after winning the support of 88 MPs.
Penny Mordaunt came second on 67 votes, with Liz Truss third (50), Kemi Badenoch fourth (40), Tom Tugendhat fifth (37), Suella Braverman sixth (32), Nadhim Zahawi seventh (25) and Jeremy Hunt in last place with 18 votes.
It means that Hunt and Zahawi drop out after failing to receive the backing of at least 30 of their fellow MPs.
It’s Mordaunt who appears to be in the ascendancy, with her surprise placing ahead of Truss coming after a YouGov survey revealing the trade minister is the runaway favourite among Conservative members.
A Sunak spokesperson: “Rishi has done well today because he is the candidate with the clearest plan to restore trust, rebuild the economy, reunite the country and because he is best placed to best Labour at the next election.
“MPs are also recognising that Rishi has the best experience and plans to deal with the current economic situation. Rishi will rebuild our economy by gripping inflation and getting our economy growing quickly again.”
David Davis, a Mordaunt spokesperson, said: “These are good results. The parliamentary results are beginning the reflect the view of the country that what we need is a reset.
“The best person to deliver that reset is Penny Mordaunt. She had a brilliant performance today at her launch, laid out an exciting policy platform and showed the command and grip to be able to deliver it.”
A Truss spokesperson said: “Now is the time for colleagues to unite behind the candidate who will cut taxes, deliver the real economic change we need from day one and ensure Putin loses in Ukraine.
“Liz Truss has the experience to deliver the benefits of Brexit from day one, grow our economy and support working families.”
Former equalities minister Badenoch tweeted: “I am grateful that so many colleagues supported me this evening.
“To win the next election and deliver Conservative solutions to today’s problems, our party must stand as the party for change.
“I have the conviction, the courage, and the clarity of thought to deliver that change.”
Steve Baker, Braverman’s campaign manager, said: “We’re very pleased with the result – we’re through and that’s good enough.”
Hunt warned the remaining candidates “smears and attacks may bring short-term tactical gain but always backfire long term”.
“A gentle word of advice to the remaining candidates: smears & attacks may bring short term tactical gain but always backfire long term,” he tweeted.
“The nation is watching & they’ve had enough of our drama; be the broad church & unbeatable, election winning machine that our country deserves.”
Zahawi did not announce his favoured candidate for the Tory leadership after he was dumped from the race.
In a statement, he said: “I am very grateful for the support of colleagues in this leadership election and to Conservatives up and down the country who have got behind me and sent me best wishes.
“Clearly my part in the contest has now ended.
“I don’t intend to make any further intervention, but I wish all the candidates in the leadership contest the very best of luck.”
The remaining six candidates will now go forward to the second round of voting tomorrow, when at least one more candidate will drop out. A third round is also expected tomorrow.
If a further vote is needed, it is due to take place next Monday, and the balloting process will continue until only two candidates are left.
The Tories’ 200,000 members will then have their say on who should be the next PM, with the result due on September 5.