Warwickshire, who had England stars Ian Bell and Jon Trott back in the side, won the toss at the County Ground in Derby and opted to bowl.
Chris Woakes got a wicket in the first over of the match, shown live on Sky Sports, when he bowled Luke Bosman with the first ball the England international faced.
In the fourth over, Woakes caught Chris Rogers who had made four and by the end of Woakes four overs at the end of the seventh over, Derbyshire were 32-2.
Chesney Hughes,was the third man out, going for a big shot and was caught by Ant Botha off the bowling of Tahir for 24, to see Derbyshire 47-3 at the halfway stage.
In the 14th over, Greg Smith pushed the run rate up with two sixes in an over which saw eighteen runs. Smith was out in the next over, caught by Rikki Clarke from the bowling of Ant Botha for 38.
Things were kept tight as Derbyshire scored seventeen off their 20th over but could only make 120-4.
Jon Trott and Neil Carter opened the batting for Warwickshire and Steffan Jones had a wicket straight away when Jon Trott, who had not scored, hooked one to John Sadler, who dived to catch.
Ian Bell came in and scored Warwickshire's first run but in the next over, Neil Carter skied one to Smith, off the bowling of former Warwicks player Tim Groenewald and was out for two to leave Warwicks on 4-2.
There had been plenty of complaints to Warwicks CEO Colin Povery about the batting of Warwickshire in recent matches and now was the time for Bell, fresh from his century for England, to come to the fore.
Bell was going for the big hits and hit two fours as Warwicks after four overs were 15-2.
He added two more fours in next over and in the last over of the powerplay over, Jim Troughton was caught by Smith off the bowling of Groenewald after making two runs for what was a wicket maiden.
The Coventry born batsman continued in his aggressive manner and by the halfway stage, he was 41 not out as Warwicks were 56-3.
Bells fifty came up from 44 balls and included seven fours and a six and the fifty partnership was sealed by a four from Darren Maddy.
By the end of the 13th over, the duo had the score down to a run a ball. The partnership ended when Darren Maddy was caught for 23 by Peterson from the bowling of Smith, so Ian Westwood came in with 38 runs from 36 balls now required.
Bell hit some more good shots but got a top edge to the wicketkeeper and was out for 66 from 56 balls to see Warwicks on 98-5 in the 15th over.
Then a sixth wicket went down as Clarke was bowled by Steffan Jones. With less than three overs to go, Ian Westwood hit a four but Botha ran out Westwood who was short of his crease as the game went into the final two overs with Warwicks still needing nine runs.
That was three runs from the final over from Greg Smith. Botha got a single from the first ball and Woakes hit a four to see Warwicks finish on 123-7 and earn a three wicket victory with Ian Bell not surprisingly man of the match.
On Friday, Warwicks are again in Twenty/20 action with a home game against Durham. Play is due to start at 5.30pm and commentary can be found on the website of BBC Coventry & Warwickshire.