Chasing a Duckworth-Lewis adjusted target of 172 for victory, Graeme van Buuren's 84 and Heino Kuhn's unbeaten 63 saw the Titans canter home in just 27.1 overs.
That put the defending champions on top of the table on net run-rate, level on points with the Dolphins and the Cape Cobras, although the Western Cape side has a game in hand.
But Van Jaarsveld kept the innings ticking and guided the Dolphins to 88 for three before rain stopped play in the 18th over.
The game was reduced to 37 overs per side when it got back underway, putting the onus on the Dolphins to get cracking, but barring a couple of big overs Van Jaarsveld and Tshepang Dithole struggled to gain momentum.
Henry Davids (3 for 30) then pulled the rug from under the visitors when he had Dithole caught and bowled and Ryan McLaren trapped lbw in the space of four balls, before having Van Jaarsveld caught behind for 66 in his next over.