Jayasuriya hit 111 from just 82 balls as Sri Lanka overhauled New Zealand's respectable 285-8 -- including an undefeated 128 from rookie Ross Taylor -- with 10 overs to spare on an ideal batting surface at McLean Park on Thursday.
Jayasuriya and fellow opener Upal Tharanga plundered the wayward attack, smashing 90 runs from the first 10 overs and hitting another 50 from the next five.
The 37-year-old Jayasuriya showed no signs of age as he hit 12 fours and five sixes in his whirlwind innings.
Sri Lankan skipper Mahela Jayawadene also gave credit for the victory to his bowlers, who pegged the New Zealand batsmen back in the last quarter of the innings.
"The comeback was very nice to see, it showed a lot of character by the bowlers and to cap it off with Sanath the way he batted was absolutely brilliant to watch," Jayawardene said.
Pace bowler James Franklin dispatched Jayasuriya and Tharanga in consecutive balls in the 25th over, bringing to an end the 201-run opening partnership.
But Sri Lanka's win was all but in the bag, with Jayawadene (34 not out) and Kumar Sangakkara (36) ensuring victory.
The absence of the home side's top bowlers, including star speedster Shane Bond who was being rested, cost New Zealand dearly.
Pace bowlers Andre Adams, Michael Mason and debutant Mark Gillespie all conceded more than seven runs an over. Left arm spinner Daniel Vettori, standing in as skipper for a resting Stephen Fleming, was the only bowler to emerge with his reputation intact, finishing with 1-36 from eight overs.
Taylor and veteran Nathan Astle (83) provided the backbone of the New Zealand innings in a 151-run partnership, which at one stage appeared likely to set up a huge total.
But New Zealand lost six wickets for 63 runs in the last 12 overs as the Sri Lanka's bowlers found the tight line which had eluded them earlier.
Vettori said his side should have been able to score 320 on the placid pitch, although he also paid tribute to the tight bowling by the visitors in the final overs. He admitted this was in stark contrast to the performance by his own bowlers.
The big-hitting Taylor, playing only his third one-day international, scored his first international century off 133 balls in a masterful innings which included four sixes and 12 fours.
The 22-year-old brought up his century in the 44th over and had to battle cramp as he struggled through to end of the innings.
"He's fulfilled some of the potential people think he does have and we've seen how he can play on a quality wicket, so hopefully that's the start of a lot of good innings for New Zealand," Vettori said.
Astle survived some shaky early overs and poor recent form to recover his swashbuckling style of old. His innings ended cruelly when bowler Jayasuriya deflected a drive from Taylor on to the stumps at the non-striker's end, leaving Astle stranded outside the crease.
The wily Chaminda Vaas with 3-50 was the pick of Sri Lanka's bowlers, taking the wickets of Vettori and James Marshall in consecutive balls to put the brakes on the New Zealand innings.
Lasith Malinga made up for a loose early spell with two late wickets for a tally of 2-66.
New Zealand 285 for 8 (Ross Taylor 128, Nathan Astle 83; Vaas 3 for 50, Malinga 2 for 66) lost to Sri Lanka 286 for 3 in 40 overs (Sanath Jayasuriya 111, Upul Tharanga 68, Sangakkara 36, Jayawardene 34 n o; Franklin 2 for 69, Vettori 1 for 36)