Centurion Joe Root guided England to a five-wicket victory over Sri Lanka at the Pallekele International Stadium.
Root shared stands of 104 with James Taylor, who made 68, for the third wicket and then 86 with Ravi Bopara for the fourth, to consolidate the fine work of Chris Woakes and others with the ball in this fifth one-day international.
England had to return on the reserve day, after rain on Wednesday, to chase 240 - and thanks chiefly to Root's 104 not out and Taylor's innings, the successful mission was rarely in doubt.
The reply did hit early trouble, with the wickets of both openers Moeen Ali and captain Cook.
But Taylor, fresh from his 90 in Colombo five days ago, responded with a calm intent to provide the initial impetus as England posted their first century partnership of this tour.
It took just 20 overs - and although Taylor then fell disappointingly, what had appeared an awkward target on a spinner's pitch never transpired as such despite a minor late wobble before Root reached his hundred with his favoured slog-sweep for a six off Ajantha Mendis to go with his seven fours from 115 balls.
England sealed the deal with five balls to spare and therefore have the chance, when they return to this ground on Saturday, to square the series at 3-3 with one to play back in Colombo.
Cook and Moeen both fell to the spin of Sachithra Senanayake, in his first match back after having his action cleared by the International Cricket Council.
Sri Lanka began with off spin at both ends, and Moeen picked the wrong ball to try to heave to leg and was bowled off stump.
Senanayake, who caused such a stir in England last summer with fine bowling and his controversial run-out of Jos Buttler backing up at Edgbaston, soon made his mark again - Cook beaten on the front-foot defence to go lbw.
The updated statistic beloved by the captain's many detractors stands at one half-century in his last 20 ODI innings.
Taylor, however, was again looking the part at number three.
He had already hoisted Tillakaratne Dilshan over long on for six, before hooking up once more with Root - after their partnership of 93 in Sunday's defeat at the Premadasa Stadium.
Once more, they profited from fine running, constantly putting fielders under pressure, and deft placement until Taylor mis-pulled Ruchira Perera straight to long leg.
He had hit five fours and that six from 90 balls by then, though, and it seemed England had surely done all the hard work.
So it proved, Bopara lending Root fresh support.
The only significant remaining question appeared to be whether the Yorkshireman would reach his third ODI hundred, all this year.
Sri Lanka put a minor late squeeze on, though, and Bopara was caught at long on.
Even so, after Eoin Morgan also holed out, England duly finished the job started 24 hours earlier by Woakes' second six-wicket haul in this format.