Warwicks had Essex on 78-6 at the close of play last night and this morning, Imran Tahir struck twice as the home side were skittled out for 159.
This left Warwickshire needing to match the 155 they made in the first innings yesterday.
James Ord was out in the ninth over for six runs but Ian Westwood and Darren Maddy took over to move Warwicks nearer the total. At tea, they needed seventy runs for victory with another session and a day to get them in.
Maddy went for 39 when he was caught by Phillips off the bowling of Masters as Westwood passed the fifty run mark. Westwood was out for 61 leaving Troughton and Clarke to steer Warwicks to victory.
Warwickshire's next match is a floodlit Pro40 game at Nottinghamshire on Thursday. Play is due to start at 4.10pm.
In the test match at Edgbaston, Pakistan were all out for 72 with James Anderson and Stuart Broad both taking four wickets along with a brace for Steven Finn. Jon Trott was 31 not out as England closed on 112-2.