Liam Livingstone was named Player of the Match after finishing the job with the bat, scoring 29no from 26 balls as England reached their revised target of 103 from 18 overs with 11 balls to spare.
England had slumped to 4-36 in the seventh over in their pursuit of the small target in difficult batting conditions but Livingstone helped them rally, alongside Sam Billings who made 24 from 29 balls, after a 40-minute rain delay at 4-69.
Earlier, Sri Lanka won the toss and elected to bat, but could only manage 7-111 from their 20 overs, with Kusal Mendis top scoring with 39 from 39 deliveries.
He combined with Kusal Perera (21) for a 50-run third-wicket partnership which had the tourists in a good spot at 2-68 in the 13th over, before fading late, unable to find any rhythm with the bat.
Mark Wood and Adil Rashid both took two wickets for England, with the former getting Mendis and the latter dismissing Perera.
England captain Eoin Morgan said: “Our bowling was right on point, both batting sides struggled to take aggressive options which is a shame, but it ended up being a tight game.
“We took risks and lost wickets, which is disappointing, but Liam showed the class he’s shown for Lancashire and Sam for Kent.
“We were juggling DLS, and being challenged by the Sri Lanka bowlers. DLS crept up on us, it was clear all morning. We were thankful we managed to reduce Sri Lanka so that it didn’t jump up on us.”
The final T20I will be played at the Rose Bowl in Southampton on Saturday.