Tournament co-hosts Sri Lanka appeared to be well set after restricting England to a below-par 9-146 in the Group 2 match at the Pallekele International Cricket Stadium on Sunday.
But Jacks, who made 21 useful runs down the order, returned to claim 3-22 as England bowled out Sri Lanka for 95 inside 17 overs to prevail.
England thus managed to succeed where Australia had failed, having lost to the co-hosts at the same venue six days earlier which effectively knocked them out of the tournament in the group stages.
"It encourages me to get into the game and perform better," player of the match Jacks said.
"Bowling in the powerplay is something I've done a lot of. So it's not foreign to me."
Sri Lanka captain Dasun Shanaka elected to field after winning the toss and had reasons to feel vindicated as England slumped to 4-68 at the halfway mark of their innings.
Jos Buttler's 14-ball struggle ended when he was trapped lbw for seven after attempting a reverse shot against spinner Dunith Wellalage only to miss a ball that rapped him on the pad.
Spinner Maheesh Theekshana dismissed the in-form Jacob Bethell for three and Tom Banton perished in his pursuit of a risky single, beaten by Shanaka's direct throw from mid-off.
Harry Brook made 14 before Wellalage dismissed him lbw, a decision the England captain challenged but could not overturn.
Phil Salt (62) raced to a 36-ball fifty -- England's key innings -- but holed out in the 15th over to give Wellalage his third wicket of the match.
Jacks added late runs but England still fell short of the 150-mark.
They needed a lion-hearted bowling effort and produced one to reduce Sri Lanka to 4-22 inside five overs.
Jacks dismissed Kusal Mendis and Pavan Rathnayake off successive deliveries after Jofra Archer sent back Sri Lanka's in-form opener Pathum Nissanka.
Archer also removed Kamil Mishara and Sri Lanka slumped to 5-34 after Wellalage became Jacks' third victim.
The hosts could never really recover and several frontline batters fell to soft dismissals, with Dushan Hemantha's bizarre hit-wicket exit for five summing up Sri Lanka's batting.
Shanaka made a defiant 30 but Jacks, completing his big day in style, relayed a catch in the deep to remove the Sri Lanka captain and effectively seal England's victory.
