Sri Lanka's 5-0 series victory was the first time England had lost a head-to-head limited overs campaign by such a margin and their tenth defeat in their last 12 One-day Internationals.
Set a seemingly imposing 322 for victory, Sri Lanka finished on 324 for two with more than 12 overs to spare.
Jayasuriya, playing a world record-equalling 362nd One-day international, scored 152, off just 99 balls, and fellow left-hander Tharanga 109, both men scoring their second centuries of the series.
Their stand, in what was the 2,389th One-day international, surpassed the 258 shared by India's Sourav Ganguly and Sachin Tendulkar against Kenya at Paarl in 2001-02 as the best opening partnership in this form of the game.
Meanwhile England spearhead fast bowler Stephen Harmison - whose first five overs cost just 33 runs - saw his 10 wicketless overs go for 97 runs.
That was the most expensive 10-over spell by an England bowler in a One-day International surpassing the 83 runs conceded by Derek Pringle against West Indies at Gujranwala during the 1987 World Cup.
By contrast Sri Lanka novice quick Lasith Malinga took a creditable four for 44 amidst all the run scoring on a good pitch.
"To finish the series on such a high note has been brilliant," said Sri Lanka captain Mahela Jayawardene, whose team battled back to draw the preceding Test series 1-1.
"Sanath is very difficult to stop when he's in that mood."
England were without several injured players, including bowlers Simon Jones, Andrew Flintoff, Ashley Giles and Paul Collingwood, but Jayawardene added: "I don't know about the casulaties, the way Sanath played today any decent attack would have gotten the same from him.
"I've seen him going against Australia, with Glenn McGrath, Brett Lee and Jason Gillespie and he has done the same thing."
Jayawardene finished on 12 not out and Kumar Sangakkara 23 not out.
Sri Lanka made a blistering start with 46 runs coming off the first three overs - at the same stage England had scored just one after two maidens from Chaminda Vaas.
Jayasuriya's hundred, his 21st one-day international century, came in 72 balls with two sixes and 13 fours and Tharanga's up in 82 balls with a six and 14 fours.
"If you get 300 on any wicket you fancy your chances, but we just didn't get the ball in the right areas," Trescothick said. "But coming up against someone like Sanath Jayasuriya in that sort of form is pretty difficult.
"It's always nice to get a hundred," he added of his own innings. "But it's irrelevant. We lost the game."
Even allowing for their injury problems, England's inability to bowl straight was a worrying sign in the lead-up to next year's World Cup in the West Indies.
Tharanga fell when he was caught and bowled by off-spinner James Dalrymple, having faced 102 balls in all and then 286 for one became 289 for two when the 37-year-old Jayasuriya, man-of-the-match and the series, was caught by stand-in captain Andrew Strauss off the part-time spin of Vikram Solanki.
Earlier, Trescothick's hundred was the centrepiece of England's 321 for seven.
The Somerset left-hander's 121 was the first by an England batsman in a one-day international since he himself made 104 not out at Headingley against Australia nearly a year ago.
Trescothick completed his hundred in 102 balls with 16 fours before he was bowled by left-arm spinner Jayasuriya.
There was a sombre note midway through the match with a minute's silence to mark the death of England fast bowling great Fred Trueman, a legendary figure at Headingley where he starred for Yorkshire.