
Jayawardene struck three successive boundaries off paceman Shanthakumaran Sreesanth to end the contest with more than one over to spare.
His efforts overshadowed a fine century from Suresh Raina, who struck 106 to rescue India from a top-order collapse as they were bowled out for 245.
Kumar Sangakkara had put Sri Lanka in a strong position with his fourth half-century in five matches. Sangakkara, who hit 55, shared a second-wicket stand of 93 with Tillakaratne Dilshan, who made 49.
Man of the match Nuwan Kulasekara (four for 48) and his new-ball partner Chanaka Welegedara (three for 53) had earlier run through India's top-order after Sangakkara won his fifth straight toss and opted to field first.
India slumped to 60 for five before a 106-run partnership between Raina and Ravindra Jadeja (38) steadied the ship. Watch cricket news live score