Nicky Morgan said "momentum" is with Michael Gove after he narrowed the gap for second place on Jeremy Hunt.
The Conservative MP told talkRADIO’s Eamonn Holmes the number of candidates still in the race adds an element of unpredictability.
“The fact that we’re going to be voting again tomorrow was not necessarily anticipated,” she said.
“I think the only thing that’s predictable about Conservative party leadership contests is their unpredictability. You just never quite know what’s going to come out of left field.”
Boris Johnson improved his lead in the third ballot, jumping 89 votes clear of his nearest rival.
Ms Morgan said whoever faces Mr Johnson in the second stage of the contest must hold him “properly to account”.
“As somebody who voted Remain in 2016 I think it is important we have a Brexiteer as the next Prime Minister,” she said
“There are two Brexiteers left in the contest, that’s Boris and Michael, and I’m going to ask them to support Michael.”
Rory Stewart supporter Richard Benyon said he was “very proud” to have been part of Mr Stewart’s idiosyncratic campaign.
“He made it interesting and he engaged with people outside Westminster, people who are not of the age profile that many Conservative members are. People whose votes we need in future elections,” he said
“He’s not going away, he’s going to continue to be a force in British politics for many years to come.”
THIRD ROUND TALLIES
Boris Johnson - 143
Jeremy Hunt - 54
Michael Gove - 51
Sajid Javid - 38
Rory Stewart – 27 (eliminated)