Perera reached his 100 in 44 balls to power Sri Lanka to a commanding 5-218, with skipper Charith Asalanka (46) chipping in with a 24-ball cameo.
New Zealand wicketkeeper Mitchell Hay took a stunning catch to dismiss Pathum Nissanka after the Sri Lankan opener had top-edged Matt Henry.
Hay ran backwards chasing the skyer and took the catch near the boundary rope. Realising his momentum was taking him across the rope, Hay hurled the ball into the air and returned to complete the catch.
Rachin Ravindra (69) and Tim Robinson (37) gave New Zealand a strong start with an opening stand of 81 before the hosts lost a clump of wickets.
Daryl Mitchell (35) hit Asalanka (3-50) for four sixes in a row but fell in the 17th over as Sri Lanka reclaimed control of the match.
New Zealand No.11 Zakary Foulkes made 21 not out off 13 balls, but the hosts eventually managed 7-211.
"Scoring a hundred is always special," Perera said after claiming the player-of-the-match award.
"When I went in to bat, I got a wake-up call in the first ball (getting hit on the head by a bouncer) and it was good to get on from there."
New Zealand seamer Jacob Duffy was adjudged player of the series for his eight wickets.
The three-match ODI series between the sides begins in Wellington on Sunday.
