Hampshire started their second innings at the Rose Bowl but came up against Chris Woakes who took five wickets.
Danny Briggs was the only player to reach double figures apart from Sean Ervine who scored 62 as Woakes who took 5-34, Darren Maddy and Imran Tahir took braces whilst there was a wicket for Andrew Miller as Hants were all out for 132.
That left Warwicks 58 to win and Ian Westwood and Varun Chopra polished them off in 16.2 overs to give Warwicks the much needed victory and their place in Division One for another season.