Electing to bat, Sri Lanka posted a commanding 271-6 with Kusal Mendis leading their charge with an unbeaten 93.
England, with several players still smarting from their 4-1 Ashes hammering in Australia, were bowled out for 252 in 49.2 overs at the R Premadasa Stadium. Overton belted 34 off 17 balls but could not take England across the line.
Earlier, Sri Lanka got off to a decent start after Pathum Nissanka and Kamil Mishara combined in an opening stand of 50.
Sam Curran removed Nissanka for 21 to break the stand and Adil Rashid (3-44) bowled Mishara round the legs before Mendis anchored Sri Lanka's innings.
Janith Liyanage provided a quick 46 before Dunith Wellalage produced an unbeaten cameo of 25 off 12 balls to power the hosts to a strong total.
England's spin quartet of Rashid, Rehan Ahmed, Liam Dawson and Jacob Bethell bowled a combined 33 overs between them.
England lost Zak Crawley for six in the third over of the innings before Ben Duckett (62) and Joe Root (61) revived their chase with a stand of 117.
England were cruising at 129-1 in 27 overs before collapsing.
Jeffrey Vandersay dismissed Duckett before Dhananjaya de Silva dealt a bigger blow when he trapped Root lbw after successfully reviewing the original not-out decision.
Pramod Madushan bowled Jos Buttler for 19 but Overton refused to throw in the towel. England's number nine hit two sixes and four fours before being undone by a Madushan full toss.
The second ODI of the three-match series is scheduled for Saturday.