England, needing 78, finished on 81 for four with Alastair Cook 34 not out and England captain Andrew Flintoff four not out, to win with more than a day to spare for what was only their second Test victory in nine matches.
Earlier, the 21-year-old Plunkett took three wickets for two runs in eight balls as England dismissed Sri Lanka for 231 before lunch on the fourth day.
He finished with a Test-best three for 17 as Sri Lanka lost their last five wickets for 12 runs and, in total, Plunkett had match figures of six for 60.
Michael Vandort was the last man out for 105 for the 26-year-old left-handed opener's second Test hundred.
England had been in a commanding position when, after Plunkett's three for 43 saw them bowl Sri Lanka out for a modest 141, Kevin Pietersen's dynamic 142 - his second hundred of the series - gave the hosts a first innings lead of 154.
And after dropped catches cost England victory in the drawn series opener at Lord's, Flintoff said man-of-the-match Pietersen had been the difference this time.
"We started well and the boys stuck to their task - but I think the difference between the teams was a special innings by Kevin," Flintoff admitted.
He also hailed the performance of Plunkett, given a chance this series along with fellow quick Sajid Mahmood after injuries to Stephen Harmison (shin) and Simon Jones (knee). "Liam got quick wickets and got better through the match."
Meanwhile Pietersen added: "I came down hard on myself from India for not converting starts - but it's fantastic to convert a couple I've had here now.
"It's a case of being positive and playing to my strengths, and it's working at the moment."
And the South Africa-born batsman also praised star Sri Lanka off-spinner Muttiah Muralitharan, who finished with match figures of 10 for 115, the 15th time he'd taken 10 or more wickets in a Test match.
"He is a great bowler and proved today he can knock me over whenever he wants to."
Sri Lanka captain Mahela Jayawardene was left to rue the fact that his batsmen had not been able to back-up Murali.
"If we could have set around 150 it would have probably been a decent total. "Our first innings total was a big disappointment - we let ourselves down after winning the toss and electing to bat on a very good wicket.
Murali, who'd taken six for 86 in England's first innings, struck fourth ball to have Marcus Trescothick lbw for nought.
But with such a small target, and a lack of bowling quality at the other end, not even Murali - who took all the England second wickets to fall on the way to four for 29 - could rescue his side this time.
Durham quick Plunkett had been unable to bowl on Saturday's rain-affected third day because of a right shoulder injury sustained while fielding Friday.
But after England captain Andrew Flintoff had made the initial breakthrough Sunday, taking Farveez Maharoof caught and bowled, Plunkett took over.
He had Chaminda Vaas taken in the gully by Paul Collingwood and next ball the Durham duo combined again to dismiss Nuwan Kulasekara. Lasith Malinga survived the hat-trick ball but soon edged Flintoff to Strauss at second slip.
Vandort became Plunkett's third victim when he was caught behind having batted for over six-and-a-half hours, facing 303 balls with nine fours.
England scored 295 on Friday as England seeked to atone for Lord's, where Sri Lanka batted for 14 hours to save the game after following-on.
His innings was particularly valuable as none of his team-mates managed more than Strauss's 30.
The third Test is due to start at Trent Bridge on Friday.