Former home secretar Mr Cleverly was eliminated in yesterday's ballot of Tory MPs, following Tom Tugendhat, who was knocked out on Tuesday.
Ms Badenoch won 42 votes and Mr Jenrick 41 votes, to Mr Cleverly's 37 votes in the latest ballot, with 120 Tory MPs having taken part.
The final round of the contest will now see Conservative Party members across the UK vote to select the successor to Rishi Sunak.
The result will be announced on November 2.
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