Warwicks batted first and Ian Bell was in superb form. The Coventry born batsman only faced 101 balls, hitting 12 fours and one six in an innings of 105.
Jon Trott made 36 with Rikki Clarke adding 33 and Ant Botha 32 as Warwicks totalled 246-6 from their forty overs.
Neil Carter had Parks and Rodger out to leave the visitors at 12-2. Hines was run out by Troughton before Carter picked up his third wicket.
Rikki Barker chipped in with a wicket as did Jon Trott who bowled Poynton for 24.
Derbyshire were now in big trouble on 121-7 and then Shanthakumaran Sreesanth mopped up the tail by taking the final three wickets to see the visitors all out for 136 in 29.3 overs and Warwicks wnners by 110 runs.
On Wednesday, Warwicks travel to Sussex in a County Championship game needing to avoid defeat. Play is due to start at 10.30am.