Jaques scored 32 not out from 18 balls and the pair took England to 161-6 with three balls remaining.
Jacques, who took 2-23 to become England’s leading bowler, was named player of the match for an incredible fourth time in seven T20 World Cups this campaign.
“I think it’s the best,” Jacques said of his growing collection of Player of the Match awards.
“I am absolutely thrilled to be not out in the end in a tough match.
“When I got there, it was on a knife’s edge, and I was over the moon.”
New Zealand captain Mitchell Santner paid tribute to Ahmed and Jacques.
“Rehaan has shown his class with the bat over the last few years and is obviously a very good player of spin,” Santner said.
“So he wasn’t really nervous on that wicket. The way Willie J and Rehan put the finishing touches on it was good batting.”