Joe Root top-scored with 93 as England made 324 for seven in the fifth and final one-day international at Cardiff.
Together with Jos Buttler, who made a typically rapid 70, he put on 109 for the fifth wicket.
Off-spinner Danushka Gunathilaka, best known as a batsman, took a career-best three for 48 as Sri Lanka looked to restore some pride, having already lost the series at 2-0 down.
Sri Lanka captain Angelo Mathews opted to bowl first after winning the toss on a green-tinged pitch.
England won Wednesday's fourth ODI at The Oval by six wickets, with opener Jason Roy scoring a superb 162 on his Surrey home ground.
Roy again looked in good touch in making a run-a-ball 34 either side of a rain-break.
But there was to be no third hundred this series after his 112 not not out at Edgbaston, with Roy hoisting paceman Suranga Lakmal to deep square leg.
Vince, opening in place of the injured Alex Hales, marked his maiden ODI innings with a stylish fifty.
But two balls after reaching the landmark Vince charged at Gunathilaka and was stumped by Dinesh Chandimal.
His exit left England 108 for two.
England captain Eoin Morgan made 20 that included a soaring six over long-on off leg-spinner Seekkugge Prasanna.
However, the left-hander also fell to Gunathilaka when he sliced the off-spinner to cover sweeper Kusal Mendis,who held a good low running catch.
It was the 21st successive innings in all international cricket where the Irishman had failed to make a fifty.
Jonny Bairstow (22) became Gunathilaka's third victim when he holed out to long on to leave England 182 for four in the 33rd over.
Buttler, scooping fours and launching Lakmal for a spectacular six over long-off, added fresh impetus with a 35-ball fifty.
The wicket-keeper dug a good Nuwan Pradeep yorker out for an off-driven four that brought up a century stand with Root in 82 balls.
His 45-ball innings ended when he was bowled by debutant Chaminda Bandara for the left-arm seamer's first international wicket.
Root then reverse-swept a Bandara full toss for four to bring up the 300.
At the start of the last over, Root - dropped on 90 - was 93 not out.
But there was to be no ninth ODI century for the Yorkshireman, as the first delivery of the 50th over saw him bowled by Pradeep to end a 106-ball knock including six fours. – AFP