It was the 18th ODI century for the master batsman who should have been run out by Mitchell McClenaghan on nine.
McClenaghan, New Zealand's hero with a triple-wicket maiden late in the innings, was the villain early on when he missed the stumps from close range with Jayawardene well short of the crease.
It was a lifeline Sri Lanka needed as Jayawardene alone looked comfortable against the New Zealand attack.
In his first match in New Zealand since retiring from Test cricket last year, Jayawardene's 104 off 107 balls included 12 fours and one six.
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He trapped Dimuth Karunaratne in front for five and Kane Williamson snared a sharp chance at backward point to claim the prize wicket of Kumar Sangakkara for four.
Sangakkara, whose departure brought Jayawardene to the crease in the eighth over, never looked at ease with a boundary his sole scoring shot from 15 balls faced.
Tillakaratne Dilshan crafted 19 before he was stumped by Luke Ronchi when he danced down the wicket to Nathan McCullum and was beaten by a well-flighted delivery.
McClenaghan came into his own towards the end when he removed Jeevan Mendis, Jayawardene and Thisara Perera in the space of four balls as Sri Lanka went from 200-5 to 200-8.
McClenaghan finished with four for 36 off his 10 overs.