MORE: Cook blames bowlers for England's Colombo loss
The hosts took a 1-0 lead in the seven-match series on Wednesday as the best efforts of Moeen, who struck 11 boundaries and five maximums in his 119 from 87 deliveries, proved in vain.
Sri Lanka had earlier made a daunting 317-6 in Colombo, thanks to 88 from Tillakaratne Dilshan and 59 from his opening partner Kusal Perera.
Mahela Jayawardene showed his customary class with a half century of his own, before Lahiru Thirimanne (27 not out) and Jeevan Mendis (30 not out) added some late impetus.
While captain Alastair Cook struggled at the start of England's reply - successfully appealing two lbw decisions in as many balls in the first over - Moeen found the boundary with regularity.
But when he was sixth out with 115 still needed off 19 overs, England looked to have a mountain to climb.
Ravi Bopara took them close with 65 from 62 balls, but it was not enough as the home side wrapped up victory with 17 balls to spare.
Dilshan and Kusal Perera made an excellent start for the home side, putting on 120 for the first wicket before the latter was run out following a terrible mix-up.
England struck a huge blow in the next over as Moeen (1-66) removed Kumar Sangakkara lbw for just two, the batsman wasting a review on a ball that was going on to hit middle and off.
Dilshan and Jaywardene set about recovering from the double setback, adding 76 before the opener was ousted by a superb return catch from Chris Woakes (2-68).
Skipper Angelo Mathews made a breezy 33 from 24 deliveries before falling to James Tredwell, who also accounted for Jayawardene on his way to taking 2-52.
Woakes dismissed for Thisara Perera (4), before Thirimanne and Jeevan Mendis provided some late fireworks - including 21 from the penultimate over - to take the hosts beyond the 300 mark.
England's reply got off to a shaky start, Cook earning a double reprieve after twice being given out to deliveries from Mathews (0-17).
Moeen then enjoyed a huge slice of fortune as a bottom edge deflected onto his pad and then onto stumps without dislodging the bails, with Mathews again the unfortunate bowler.
After Cook's departure for 10, Mooen and Ian Bell added 56 before the latter became the first of Thisara Perera's three victims for a run-a-ball 35.
Joe Root (2) and Eoin Morgan (1) both went cheaply, before Jos Buttler (21) was fifth out with the score on 159.
After the demise of Moeen, Bopara failed to gain sufficient support from the tail, and was eventually last man out when he skied a chance to Kusal Perera, who took a well-judged catch diving forward to seal victory.