Set 343 to win off 58 overs when England declared its second innings on 335-7, Sri Lanka never attempted to chase a target that was near impossible with captain Tillakaratne Dilshan able to bat only in an emergency because of a broken thumb.
Sri Lanka resumed the final session on 32-1 and took few risks, comfortably surviving the loss of Mahela Jayawardene for 25 and opener Tharanga Paranavitana for 44.
England had won the first test after a similar declaration, putting the tourists in for 50 overs in Cardiff and bowling them out for 82 for an innings victory.
"We thought we had a chance if we took early wickets," England captain Andrew Strauss said. "We needed something special to happen and it didn't quite happen for us.
"But I'm very pleased from the way we came back from being 22-3 on the first day. There's a lot of positives to take out of it. It wasn't the best test match we have ever played but we move on to The Rose Bowl and hopefully we can make it 2-0."
Alastair Cook's 18th test century for England and the early loss of stand-in opener Kumar Sangakkara - out for 12 when he miscued a cut off Chris Tremlett to Eoin Morgan at cover point - had left Sri Lanka facing a nervous final session with 45 overs remaining.
But an unadventurous run rate of 2.95 per over used up plenty of time, with Jayawardene taking 71 balls for his 25 before falling when he drove at a wide delivery from Stuart Broad to Kevin Pietersen at fourth slip.
An inswinger from part-time bowler Jonathan Trott trapped Paranavitana lbw, reducing Sri Lanka to 96-3, but Thilan Samaraweera finished 17 not out after successfully reviewing an lbw decision on 4. Umpire Billy Doctrove initially gave him out not offering a shot to a ball that pitched well outside off stump.
Prasanna Jayawardene inched his way to 12 with 15 overs remaining at the close.
"All round it was a good performance after the Cardiff match," Dilshan said. "At the moment, I believe I'm going to miss the last test match but we'll see over the next couple of days."
Sri Lanka now needs to win the June 16-20 third test at The Rose Bowl to salvage the series, but is almost certain to be without man-of-the-match Dilshan.
Dilshan did not field or open on Tuesday after the thumb on his bottom hand was struck twice by Chris Tremlett during his first-innings 193. He was hit on Saturday when on 55 and set a test career best the following day before Tremlett struck him again, bending his already taped thumb back toward the wrist.
Dilshan added only one more run before falling for by far the highest score in Sri Lanka's 479 all out.
With Sangakkara now averaging 26.60 in eight innings in England, Dilshan's injury could rob Sri Lanka of much of its batting prowess.
"We have 10 days until the next test match," Dilshan said. "The doctors advise to rest three to four weeks, but we'll see how we go."
Cook and Pietersen, with 72, helped take England from an overnight 149-2 to a commanding 305-3 before four wickets tumbled for 30 runs as the home team took risks in hope of setting a challenging total.
Cook was stumped by Prasanna Jayawardene for 106 in the fifth over of the session, Eoin Morgan holed out for 4 in the next and Matthew Prior was run out for 4 in the next.
Furious at his cheap dismissal, Prior had to apologise to members of the Marylebone Cricket Club after his bat broke a window back in the dressing room and showered them with glass.
"It was one of those unfortunate incidents," Strauss said. "Matt Prior didn't mean to break the window at all. But it was dangerous and we apologised."
Ian Bell gave England's innings a surge as he raced to 57 from 43 balls for his 27th half century, before Strauss called the players back in when Stuart Broad was caught behind off Dilhara Fernando for 3.
Cook and Pietersen had started the day reasonably briskly, adding 61 in the first hour as the hitherto economical Chanaka Welegedara conceded 12 runs from each of his second and third overs, but slowed as cloud obscured the bright sunshine in the hour leading to lunch.
That slowdown cost England a few runs or more time to bowl at Sri Lanka, but England can look happily upon the continued good form of Cook and Bell - and a possible resurgence by Pietersen.
"He played really well," Strauss said. "As we always said, it was just a matter of time."
Having managed just 2 in the first innings, Pietersen had come to the crease with England on 117-2 and just one three-figure score in his last 34 innings.
He moved swiftly from his overnight 15 with a series of front-foot drives against the medium pace of Welegedara and Suranga Lakmal.
The scoring slowed during Rangana Herath's overs and the left-arm spinner troubled Pietersen enough to force an inside edge on to the pad that landed safely when he was on 37.
He made it to 50 off 85 deliveries and looked like he may reach his hundred, but Herath got one to turn out of the rough outside leg and beat his defense to hit the off stump.
After scoring centuries in his first two matches against Sri Lanka five years ago, his 124-ball knock was his highest score in 12 test innings against the tourists.
Meanwhile, Cook passed India great Sachin Tendulkar as test cricket's leading scorer over the past 12 months.
Cook, who hit 96 Friday in England's first-innings 486, added 45 runs to his overnight score and has now scored 1249 runs over the past 12 months. Tendulkar is next with 1245 and Trott third with 1112.
