The 22-year-old left-hander shared a 110-run stand for the third wicket with Kevin Pietersen (63 not out) to give England a memorable win in the day-night game.
England last won a one-day series in the subcontinent in 1986-87 when they beat Pakistan 3-0.
After restricting Sri Lanka to a modest 211-9, England reached the target with 19 balls to spare for an unbeatable 3-1 lead in the five-match series.
"The boys bounced back brilliantly after the defeat in the first one-dayer. Credit to the players, the coaches, everyone worked hard.
It is great to win this series," England skipper Paul Collingwood said.
"The conditions were very difficult and the way our bowlers put their batsmen under pressure despite losing the toss, they deserve a special mention.
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Sri Lanka owed their total to gritty half centuries by Kumar Sangakkara (69) and Chamara Silva (67). The duo shared a 126-run stand for the fourth wicket to bail the side out after they were tottering at 20-3.
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