Banton scored 126 after England chose to bat and laid the foundation for a formidable total of 7-355 before they dismissed Sri Lanka for a modest 132.
Banton's innings, which highlighted his expansive range of shots, included five sixes and 16 fours as he mercilessly took to the visiting bowling once fellow opener Ben Duckett had been castled in the second over.
England captain Harry Brook, who was dropped when he had seven runs, also punished Sri Lanka's poor fielding with 77 off 66 balls while Jordan Cox, replacing the injured Jos Buttler, made 76 from 52 on his return to the ODI side for the first time in almost two years.
"I thought it was a near-perfect performance with everyone chipping in beautifully," said Brook.
England had won the first ODI at Chester-le-Street on Tuesday by 89 runs but lost by 16 runs in Leeds two days later, setting up Sunday's decider which turned into a one-sided contest with Sri Lanka bowled out in 29.1 overs.
Sonny Baker took two balls on his second ODI appearance, one year after his debut, to snag the wicket of Pathum Nissanka, who touched one behind to wicketkeeper Cox, beginning a steady stream of dismissals.
Six of the seven bowlers that England used got among the wickets, with Liam Dawson finishing with 3-26 in eight overs and Gus Atkinson taking 2-26 from five overs.
Captain Kusal Mendis, who scored a ton in the second ODI, top-scored for the visitors with 36 but Sri Lanka never looked like being able to chase down the imposing target.
"I think we've only lost two white-ball games all summer, so this group's doing incredibly well, improving, learning all the time, and moving in the right direction with the World Cup around the corner," said Joe Root after picking up an award as England's best ODI player of the summer.
"I think we're trending in a really good way so long may that continue, and that hunger stays there, and we can keep winning match-winning performances and series wins before that comes round."
