Jos Buttler struck a blistering unbeaten 66 to power England to a commanding 171 for four after they had made a slow start.
The 2010 winners then returned to blow away Sri Lanka's top order before Angelo Mathews fought off a hamstring injury to drag his team back into the match with a brilliant 73 not out.
Sri Lanka's defeat also dashed South Africa's hopes of qualifying for the last four.
"I think we adapted a lot better today than we did against Afghanistan," said England captain Eoin Morgan, referring to his team's mediocre batting display in their previous match.
"We showed we're capable of playing both smart cricket and aggressive cricket."
Put in to bat, England lost Alex Hales in the second over but Jason Roy (42) and Joe Root (25) added 61 runs in 8.3 overs to steady the innings.
Leg-spinner Jeffrey Vandersay dismissed both batsmen but Buttler capitalised on the foundation, hitting eight fours and two sixes in a 37-ball blitz.
Morgan made 22 before being run out and Ben Stokes smashed the last ball, the only delivery he faced, from Thisara Perera for six.
Sri Lanka made a dismal start to their reply as openers Tillakaratne Dilshan and Dinesh Chandimal were dismissed inside the first eight deliveries.
Milinda Siriwardena and Lahiru Thirimanne also went as Mathews' side slumped to 15 for four.
Skipper Mathews and Chamara Kapugedera (30) revived their hopes, mixing caution with aggression and smashing three sixes off an Adil Rashid over that produced 21 runs.
Perera also scored 20 quick runs down the order but Mathews looked tired by the end and could only score four of the 15 runs required from the last over by Stokes.
"We had nothing to lose after we were 15 for four," said Mathews. "Myself and Kapugedera decided we'd target a few bowlers.
"It worked but unfortunately I didn't have a (frontline) batter with me in the last couple of overs. It was a really good wicket...if we had another batter we could have got over the line."
Buttler was named man-of-the-match for his typically belligerent knock.
