Jos Buttler made an unbeaten 73 and Eoin Morgan hit 47 not out as England eased to their target of 141 with more than two overs to spare.
Willey and Plunkett shared seven wickets after the Root-Buttler stand laid the platform for a 122-run victory.
Jason Roy smashes 162 as England gun down 306 in just 40.1 overs to pocket the ODI series.
Persistent rain prevents a result between England and Sri Lanka in the third ODI at Bristol on Sunday.
Alex Hales scored 133* and Jason Roy 112* as England chased down Sri Lanka's 254 without losing a wicket, a record in ODIs.
England were in trouble at 82/6 at one stage in chase of 286, but Jos Buttler's 93 and Chris Woakes' 95 helped the hosts settle with a tie.
Clinical Sri Lanka ease past Ireland by 136 runs in 2nd ODI, with this win Sri Lanka have completed a 2-0 series win against Ireland and have the momentum going into the series against England.
Dinesh Chandimal's unbeaten century helped Sri Lanka secure a 76-run victory over Ireland in the first one-day international at Malahide on Thursday.
England also named uncapped Dawid Malan, Tymal Mills and Liam Dawson in T20I squad with Joe Root and Alex Hales rested.
England were denied the chance to press for a series whitewash over Sri Lanka as rain ruined the final day of the third Test at Lord's on Monday.