Hornchurch opener George Hankins was the difference between the two sides as his knock of 84 off 24 balls set the foundation for their win over Old Victorians.
He hit 13 sixes as he and Lesbourne Edwards put on 97 runs for the second wicket before Hankins was trapped lbw by Jenner towards the end of the sixth over with the Londoners on 112-2.
Theo Pullman and Zac Wilson each took two wickets as three more Hornchurch batters reached double figures as they ended their 10 overs on 173-7.
With qualification already assured the islanders changed their line-up and lost Alistair Webster and Scott Simpson for ducks in successive second-over balls off Harry Hankins' bowling to leave OVs on 16-2 after 10 deliveries.
Opener Zac Wilson and Jenner had a third-wicket stand of 55 before Jenner was caught for 25.
Wilson went on to make 79 off 31 balls with nine sixes before he was dismissed with the final delivery of the game as Old Victorians ended on 134-8.