Warwicks batted first and Jon Trott and Neil Carter put on 96 for the opening wicket before Carter was bowled by White for a total of 68 which included two sixes.
Trott went for 33 before Ian Bell and Jim Troughton added 46 for the third wicket. The Coventry born batsman kept going as Troughton (19), Maddy (1) and Westwood (13) lost their wickets and had scored 72 from 58 balls when he became the sixth Warwickshire player to lose their wicket.
Warwicks were then on 217-6 and Rikki Clarke made a rapid 23 before Tim Ambrose (31 not out) and Chris Woakes (49 not out) steered The Bears to 321-7 at the end of their forty overs.
The visitors had a good crack at the total with James Taylor making 92 and , Paul Nixon 40 as Leicestershire needed 94 to win with 5.5 overs remaining.
However, bad light stopped play, preventing The Bears from getting the three wickets they needed and Warwicks were awarded a win by 41 runs under the Duckworth/Lewis method.
On Tuesday, Warwicks are in County Championship action against Kent at Canterbury. Play is due to start at 11am and commentary can be heard on the BBC Coventry & Warwickshire website.