With nothing to lose, Croatia’s reply started superbly as openers Sam Houghton and Connor Carroll smashed a 57-run partnership off 3.4 overs.
Houghton was caught and bowled by Julius Sumerauer for 22 off 12 balls as the pair hit 28 off Dominic Blampied in the second over.
Big-hitting Carroll – who had conceded 63 runs off his four overs with the ball without taking a wicket – seemed determined to make up for it with the bat as he reached his half-century in 16 balls.
He helped the Croats reach 87-2 at the end of the sixth over as his side kept in touch with the run rate.
Jersey thought they had taken his wicket midway through the eighth over but skipper Charles Perchard dropped a simple catch with Carroll on 69 from 27 balls.
But he was caught in the next over as Jenner held on at the boundary off a George Richardson delivery, Carroll departing having made 74 off 31 balls including nine sixes to leave Croatia on 116-3 after 10 overs.
With Carroll back in the pavilion, Croatia’s run chase slowed – Rashid Hashmi was caught for 20 and Jared Newton for 23 as they slipped to 154-5 with five overs to go.
Zak Tribe helped mop up the lower order with figures of 3-13 as Croatia were bowled out for 171 with an over to spare.