Sri Lanka chasing an imposing score of 282 for victory in 50 overs, reached their target in 49 overs when Upul Chandana lofted Zimbabwe captain Alistair Campbell for six over long-on.
Sri Lanka thus made a clean sweep of the one-day series as well winning by a margin of 3-0 to follow their 2-0 whitewash of the Test series.
Jayasuriya set the tone for his side, by cracking one six and 13 fours in reaching his seventh century in his 150th one-day international. The hard-hitting left-hander faced 100 balls in scoring 102.
With young Mahela Jayawardene contributing a stylish 74 off 80 balls with five fours in the middle-order, Sri Lanka maintained their required rate of 5.64 runs per over to overhaul Zimbabwe's massive total and retain their status as good chasers of a target.
After the dismissal of these two batsmen, Ruwan Kalpage (37 off 50 balls) contributed successfully towards the winning total, to keep up the momentum by running sharp singles to pressure on the Zimbabwe fielders.
Zimbabwe winning the toss and taking first lease of the wicket, enjoyed their best batting on the tour, when they rattled up 281 for six in 50 overs.
Grant Flower, the scorer of 17 fifties finally broke the shackles to record hiis maiden one-day century when he pulled leg-spinner Chandana for his ninth four. He was fortunate to be let off by Jayasuriya at two and at 18, but made full use of the lapses to give Zimbabwe a chance of recording their first win on the tour.
Zimbabwe based their innings largely on Grant's innings of 112 scored off 138 balls with nine fours. He shared an opening partnership of 82 with Craig Wishart (45) and a further stand of 144 for the third wicket with brother Andy Flower, who made 68 off 70 balls with five fours.
Jayasuriya took the 'Man of the Match' as well as the 'Man of the Series' awards to round off an excellent day for him on the field aftrer and inauspicious start, when he lost the toss, put down two chances and conceded 66 runs off his 10 overs.
Overall, it was a fine performance from a make-shift Sri Lanka side who were minus captain Arjuna Ranatunga, vice-captain Aravinda de Silva, Roshan Mahanama, Marvan Atapattu and Muthiah Muralitharan.
Sri Lanka gave caps to two new players in one-day cricket - Avishka Gunewardena and Naveed Nawaz, both of whom failed to make any impression.
Zimbabwe completed their one month stay in Sri Lanka failing to record a single win in their seven-matches.