The Conservative Party's 121 MPs voted to oust the former home secretary in the first round of votes.
Mr Jenrick picked up 28 votes while bookies' favourite Kemi Badenoch came second with 22.
Shadow Home Secretary James Cleverly was one vote behind on 21; Shadow Security Minister Tom Tugendhat got 17; and Shadow Work and Pensions Secretary Mel Stride picked up 16. Dame Priti got 14.
The second round of voting will be held on Tuesday before the final four take their campaigns to the Tory conference starting on September 29.
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