RAND gained an early advantage on the rest of the competition by defeating TRYC in Saturday's opening round at Rand.
With the other four matches called off due to rain, the Pigeons made 161 and won on the Duckworth-Lewis system with the visitors 5-87 off 29.5 overs.
TRYC needed to be 113 when rain stopped play.
"We were really happy to make 161 considering it was our first hit out," skipper Bryce Swift said.
"We needed to bowl 20 overs for it to be a game and thankfully we got it in."
TRYC's Todd Hannam kept his side in the match with 42 not out but a steady flow of wickets worked against the visitors.