The Sri Lanka captain, dropped twice, made 100 after scoring an unbeaten 126 at the Riverside on Saturday where the 1996 world champions took an unbeatable 3-0 lead.
Together with opener Upul Tharanga (60) he put on 137 for the second-wicket.
England fought back before an unbroken eighth-wicket stand of 68 in 38 balls between Farveez Maharoof (58 not out) and Malinga Bandara (28 not out) led the visitors past the 300-mark.
Defeat, with eight balls to spare, was injury-hit England's ninth in 11 One-day Internationals, their hopes of salvaging something from this series now resting with Saturday's finale at Headingley.
But the problems that continue to plague them in limited overs cricket, and threaten to derail their chances at next year's World Cup in the Caribbean, were evident here with England bowling 21 wides and none of their batsmen scoring a fifty let alone a hundred.
England's openers made a positive start to chasing their victory target of 319 with Marcus Trescothick and fellow left-hander Alastair Cook, on his one-day international debut, putting on a run-a-ball fifty stand.
But on 44 Trescothick, dropped on 18, chipped Lasith Malinga straight to Bandara at mid-off and, six balls later, 77 for one became 85 for two when Cook played on to Dilhara Fernando for 39.
England stand-in captain Andrew Strauss and Ian Bell rebuilt the innings with a stand of 76 before both exited on 161.
First Strauss edged off-spinner Tillakaratne Dilshan through to Sangakkara for a run-a-ball 45.
And two balls later leg-spinner Bandara had the unlucky Ian Bell, on 30, stumped by Sangakkara after the keeper dropped the ball.
Sangakkara was far tider when, after recalled batsman Vikram Solanki (10) charged down the pitch, he neatly completed a low stumping chance which left England 178 for five in the 35th over and out of the game.
Fittingly Jayawardene took the catch that ended the match when Liam Plunkett holed out off Malinga, England 285 all out.
Earlier, recalled seamer Kabir Ali bore the brunt of Sri Lanka's late assault.
His 10 wicketless overs cost 77 runs and there were 20 off his last, including two sixes by Maharoof - the first taking him to a maiden one-day international fifty off just 47 balls.
Bandara faced 21 balls with a six off Kabir and three fours. Kabir's day went from bad to worse when he was later run out first ball.
After bowling 44 wides in the first two matches of this series, England cut down to six at the Riverside. But here they sent down 21, nine from senior quick Stephen Harmison alone.
England, with the series lost, made four changes. Cook came in for the injured Kevin Pietersen (knee), Solanki replaced Paul Collingwood (thigh), Kabir took over from dropped quick Sajid Mahmood and seamer Tim Bresnan returned at the expense of off-spinner Alex Loudon.
After Jayawardene won the toss, veteran left-hander Sanath Jayasuriya, who came into the match with more one-day caps, runs, hundreds, fifties, wickets and catches then the entire England team combined, fell for 14 when a trademark cut off Harmison caught by James Dalrymple.
England then saw leg gully Bell drop Jayawardene on seven and on 27 he was missed again by Dalrymple at point.
Jayawardene pressed on to an 82-ball hundred with nine fours, a pulled boundary off medium-pacer Bell taking him to his eighth century at this level and fourth against England.
But to his next ball Jayawardene gave off-spinner Dalrymple, who took a creditable two for 44, an easy return catch.
Fall of wickets: 1-23, 2-160, 3-173, 4-196, 5-214
Did not bat: L Malinga, D Fernando
England: Marcus Trescothick, Alastair Cook, Ian Bell, Andrew Strauss (capt), Vikram Solanki, James Dalrymple, Geraint Jones (wkt), Tim Bresnan, Liam Plunkett, Kabir Ali, Stephen Harmison
Toss: Sri Lanka
Umpires: Billy Doctrove (WIS), Nigel Llong (ENG)
TV umpire: Mark Benson (ENG)
Match referee: Clive Lloyd (WIS)
June 20, The Oval: Sri Lanka won by 46 runs
June 24, Riverside: Sri Lanka won by 8 wkts
July 01: Headingley