The left-handed opener cracked 107 for his 28th hundred at the age of 39 years and 212 days, beating the previous oldest century-maker, Englishman Geoff Boycott at 39 years and 51 days (v Australia at Sydney in 1979).
Jayasuriya also became the second batsman to complete 13,000 runs in one-dayers after India's Sachin Tendulkar (16,422) during his 114-ball knock, which included one six and 10 fours.
He bolstered the innings with a 118-run stand for the second wicket with Kumar Sangakkara (44) and 51 for the next with Thilina Kandamby (17) after the opening-over dismissal of in-form Tillakaratne Dilshan.
Dilshan, who scored a century in his team's series-clinching win in his last match in Pakistan recently, was run out for no score following a mix-up with Jayasuriya.
India, who elected to field after winning the toss, then had to wait for more than 27 overs for the next success as Jayasuriya and Sangakkara applied themselves well on a slow pitch.
Jayasuriya went for big sho