Chasing a target of 156, KKR were 83 for one after nine overs when heavens opened. The D/L par score at that time was 61 for one and KKR were well ahead courtesy Gambhir and Kallis.
Gambhir-led side are second in the table with four points after four games while Warriors are leading the table with four points and a better net run rate.
Earlier, the first game between Somerset and South Australia Redbacks were abandoned with out a ball being bowled due to the rain.
KKR were off to blazing start getting 58 runs in the first Powerplay. After losing opener Manvinder Bisla (19), KKR were back in the hunt with Kallis and Gambhir, adding the firepower to propel the team into safety, stitching an unbeaten 33-ball 48 run partnership for the second wicket stand.
Gambhir was dropped by Kelly Smuts on 21 off Johan Botha while Kallis was on 15 when wicketkeeper Mark Boucher dropped him.
After being put into bat, Warriors set a decent target 155, courtesy half century from Collin Ingram.
Warriors made the best use of the conditions, with their top-order, clobbering the Kolkata bowlers. Ingram and Jon-Jon Smuts stood tall as Warriors recovered from an early loss of Ashwell Prince (4), who departed at 15.