Jeremy Hunt secured 54 votes and Michael Gove 51.
Boris Johnson again secured an easy victory with 143 votes.
Tomorrow the final candidates will be whittled down to just two, with votes in the morning and evening.
Then the final two will spend several weeks travelling across Britain for a series of hustings before a final vote.
Rory Stewart said on Twitter just moments after the result: “I am so moved and inspired by the support I have received over the last few weeks.
“It has given me a new faith in politics, a new belief in our country. I didn’t get enough MPs to believe today – but they will.
“I remain deeply committed to you and to this country. #RoryWalksOn”
Mr Javid gained five extra votes from the last round, Mr Gove gained 10, Hunt eight and Johnson 17.
Mr Stewart was the only candidate to lose votes, shedding 10 votes.
After topping the ballot for a third time, Boris Johnson tweeted: “Thank you once again to friends and colleagues for your support in the third ballot – especially on my birthday!
“We’ve come a long way but we have much further to go.”
Sajid Javid tweeted: “Delighted to make it through to the final day of MP voting. Grateful for the support of many excellent colleagues. We can do this!”
Meanwhile, Jeremy Hunt wrote on social media: “Three times now MPs have chosen me as the person best-paced to take on Boris. If I make it to the final I will put my heart & soul into giving him the contest of his life: in politics today the unexpected often happens. The stakes too high to allow anyone to sail through untested.”