The 2006 Champions had been skittled out for 151 and were following on for the first time since 2006.
Carl Hopkinson added a half century but the Hove based side lost six wickets for 41 runs and were all out for 206. A total which gave Warwickshire a win of an innings and 34 runs.
Warwicks travel to Old Trafford to play Lancashire in a Friends Provident game on Sunday.