Kumar Sangakkara top-scored for Sri Lanka with a knock of 44 runs from just 26 balls during his side's innings.
They eventually made 182 runs from their 20 overs for the loss of four wickets.
Zimbabwe struggled throughout their reply, with four of the batsman being dismissed for ducks.
Ajantha Mendis was the main wicket-taker for Sri Lanka, claiming six for just eight runs as Zimbabwe were all out for 100 runs.
The other nation in the group is South Africa.