In the third round of MP voting, Cleverly took 39 of the 120 votes, above Jenrick on 30 and Kemi Badenoch on 29. Tom Tugendhat came fourth, with 20 votes, becoming the latest candidate to be eliminated.
In the previous round, Cleverly had finished joint fourth with Tugendhat on 21 votes. He now seems a near-certainty to reach the final two in today's final choice by MPs, with Tory members then selecting the winner in a ballot.
The final result will be announced on 2 November.
Jenrick had topped the previous two MPs' votes and was seen as a virtual shoo-in for the last two. But after an underwhelming performance at the Conservative party conference last week, his support among MPs fell from 33 to 31.
He now has a desperate fight to recover some momentum and see off Badenoch, who gained two votes, as the representative of the Tory right.
Badenoch, the shadow housing secretary, seized on Jenrick's faltering campaign, with a spokesperson saying: "There are three candidates left in this contest, two are gaining votes and one is going backwards and losing support. The right of the Conservative party now needs to coalesce around Kemi."
A source in Jenrick's campaign insisted, however, that he was "in prime position to make the final two", stressing the endorsements he had received from MPS on both the right and the centre of the party.
But with Tugendhat eliminated, Cleverly is the sole remaining centrist, and seems likely to pick up some of the shadow security minister's supporters. With 121 Tory MPs in all, and Rishi Sunak having said he will not vote, even gaining two more MPs would guarantee Cleverly a place in the last two.
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