Recalled as a batsman who can bowl legspin, Denly undermined Sri Lanka's chase for 188 to win by bowling openers Kusal Mendis for 1 and Niroshan Dickwella for 3 in his first two overs.
Fellow legspinner Adil Rashid added three wickets in his first three overs, and Sri Lanka was reduced to 77-5 in 11 overs.
Captain Thisara Perera tried to revive his side with 57 off 31 balls, including six sixes, but defeat was certain by the time he clobbered a Denly full toss to midwicket in the 20th over. Denly added Lasith Malinga off the last ball, and was named man of the match in his first appearance for England since 2010.
Put into bat first up, Jason Roy gave England a lively start with a six off Malinga's second delivery.
Roy survived a run out and four dropped catches to score 69 off 36 balls, including six sixes and four boundaries. He was out in the 11th over, at 107-4.
There was a delay for rain, then England was pushed along by Moeen Ali, who hit 27 off 11, and Denly, with 20 off 17. Add on Ben Stokes' 26, and they made sure the total was competitive at 187-8.
England won the one-day international series 3-1, and the first of three tests starts on Nov. 6 in Galle.