Resuming at their overnight score of 137 for three, Middlesex could add only 109 more runs before being bundled out for 246, with Ashley Giles being the wrecker in chief taking 6-91.
Set a target of 115, the Bears lost three quick wickets of Nick Knight, Mike Powell and Jonathan Trott.
However, the in-form Ian Bell followed up his first innings 231, with an unbeaten 47 to steer Warwickshire home.
Giles, who has got off to a flyer has already taken 24 wickets this season.
Warwickshire has now three wins a now and has remained unbeaten in the competition so far.