Chasing 309 for a win at the Westpac Stadium, Sri Lanka looked comfortable from the very start after a 100-run opening partnership and then Thirimanne (139 not out) and Sangakkara (117 not out) managed an unbeaten 212-run stand to help the islanders canter to their target in 47.2 overs.
The duo combined well to make the James Anderson-led bowling attack not only look ordinary but also put up a commanding batting display in their record second-wicket partnership against England in ODIs.
Opener Tillakaratne Dilshan (44) was the only casualty in an otherwise supreme batting show - off-spinner Moeen Ali being the beneficiary of the lone wicket to fall.
The 25-year-old Thirimanne, who was dropped on 3 off Stuart Broad in the 4th over of the innings, capitalised on the spill to become the youngest Sri Lankan to score a century in a World Cup.
His 143-ball knock was studded with 13 fours and 2 sixes - hit the winning six. Sangakkara showed his class once again to register a chanceless 23rd ODI hundred, his 86-ball knock laced with 11 fours and 2 sixes.
Sri Lanka though were guilty of dropping more than a couple of catches in the England innings but their effort with the bat put a curtain on all the shortcomings.
Earlier electing to bat, England rode on Joe Root's 121 to post 309 for six in 50 overs and a quickfire 19-ball unbeaten 39 from Jos Buttler in the end raised English hopes of a good showing.
But that was not to be as Sri Lanka looked unfazed after what looked an ordinary bowling effort, to make the chase look simple and register their third win of the tournament.
After losing their opener against New Zealand, the Angelo Mathews-led side side has certainly done well to post three wins on a trot, against Afghanistan, Bangladesh and now England. The Eoin Morgan-led side on its part is struggling with just a single win from four matches and that too has come against minnows Scotland.