Warwicks put Glamorgan into bat at the Swalec Stadium in Cardiff and fielded the same team which beat Worcestershire yesterday.
Their first wicket came when Cosgrove chipped to mid-off and was caught by Westwood off the bowling of Neil Carter for 13 with the score on 27 in the fifth over.
In the seventh over, Ant Botha took the wicket of Tom Maynard to leave the score at 47-2.
Twenty more runs were scored by the halfway stage as Warwicks kept the bowling reasonably tight.
Wright was the next man out when he was caught plum LBW by Jeetan Patel for 12. That became 99-4 when a flying catch by Ian Westwood had Wallace out for six.
Jamie Dalrymple completed his half century in the fifteenth over but in the next over, he went for a big shot and was caught on the boundary by Ant Botha.
Michael Powell failed to take the score on when he was caught by Bell off the bowling off Barker to leave Glamorgan on 118-6.
Neil Carter got his second wicket and third when he took the stump of Watkins and then next ball he bowled Harris with a ball that hit the off stump as Glamorgan finished on 129-8.
Warwicks again started well but lost Neil Carter for 14 when he was bowled by Kruger. Then Kruger took the wicket of Jim Troughton for one.
Trott and Ian Bell took the score past the fifty mark in the eighth over with some good shots.
The pair put on 72 before Bell was caught behind by Wallace for 42 from 35 balls. Tim Ambrose came in next but needing only seven to win, Jon Trott ran himself out for 55.
The scores were tied going into the final over but it only needed one ball for Ian Westwood to hit a four and give Warwickshire a six wicket victory.
Warwickshire are at home to Northamptonshire on Monday. Play starts at 5.30pm.