Speedster, Zoysa, Nuwan Kalusekera and Upul Chandana scalped two wickets each as the home side hit up 220-7, while Sri Lanka lost Kumar Sangakkara second ball early on.
The visitors made a solid start to the game as Zoysa dislodged openers Craig Spearman and Jamie How with the new cherry.
Central Districts slipped into further trouble when Zoysa caught Mathew Sinclair for five off the bowling of Farveez Maharoof leaving the local side lurching at 43 for three.
Big man Jacob Oram hit a fluent 74 off 78 balls. Ross Taylor gave him support making 36 before retiring hurt. Skipper Glen Sulzberger also chipped in with 39.
Ewen Thompson gave the innings a final flourish clouting a six in his hurricane unbeaten 30 which came off only 19 balls.
The tourists now move on to Hamilton to play Northern Districts on Thursday-their final warm game before the ODI of the five-match series against New Zealand on Sunday.