In a must win game in front of a large crowd, Warwicks lost the toss and were put into bat.
Neil Carter hit a six and a four before being dismissed for ten but Jon Trott and Jim Troughton started to find runs with the bat.
By the end of the tenth over, the one hundred run mark had been achieved but Trott, who had become the highest run scorer in Twenty/20 cricket this season, was run out for 38 (six fours) to leave the score on 101-2.
Tim Ambrose was out for nine before Warwicks hit eighteen runs in one over.
Jim Troughton past the fifty mark before he became the fourth Warwickshire batman to lose his wicket when he was caught for 62 hooking out to the long boundary. That ended a partnership of 46 with Rikki Clarke, who hit four consecutive fours in the 19th over.
Westwood skied the ball on the opening ball of the final over and was caught on the boundary. Clarke made his first ever Twenty/20 half century as Ant Botha was run out on the final ball to see Warwicks close on 193-6.
Somerset started well before Langer was caught by Ant Botha off the bowling of Rikki Clarke. Marcus Trescothick made 39 and Zander De Bruyn forty as they closed down on the target.
They needed seven runs to win off the final over but some excellent bowling by Jeetan Patel saw five singles come off the over plus the vital wicket of Kieswetter who had scored 39 runs to ensure that Warwickshire were in the Quarter-Final draw along with Somerset who were the third best placed side.
That draw sees Warwickshire travel to Sussex on either July 27,28 or 29th.
On Wednesday, Warwickshire take on the England national team who are preparing for the Ashes. Commentary can be heard on BBC Coventry & Warwickshire.