Jayawardene, in sparkling form, helped Sri Lanka reach 173 for seven in their 20 overs before rain limited Zimbabwe to just five overs in reply.
Jayawardene opened the innings and dominated from the outset, scoring 10 fours and four sixes before he went in the penultimate over having reached his century in 64 balls.
The classy former skipper had helped Sri Lanka make a blistering start bringing up 50 in just 5.1 overs and 100 inside 12 overs but found it slower going later in the innings.
Jayawardene's century was the second of this tournament following Indian Suresh Raina's against South Africa on Sunday.
In reply Zimbabwe's chase ran into a rain-interruption after the first over from Ajantha Mendis.
Play did resume after 66 minutes with the minnows chasing a revised victory target of 104 runs from 11 overs but another weather-disruption greeted them four overs later when they were 29 for one.
Consequentially the Duckworth-Lewis method was invoked and Zimbabwe were found 14 runs behind their opponents.