Hampshire 285 (Wheater 57, Berg 54, Rankin 3-55, Clarke 3-66) and 283 for 3 dec. (Vince 125*, Carberry 91) beat Warwickshire 125 (Edwards 5-32, Crane 5-35) and 227 (Edwards 4-55) by 216 runs
Fidel Edwards bagged a nine-wicket haul for the match as Hampshire won their first County Championship match at the Ageas Bowl in 2015.
West Indian fast bowler Edwards took two of the four morning scalps - ending with figures of nine for 87 - as Hampshire, forced to bowl spin because of woirsening weather, beat the rain by moments.
The victory boosts Hampshire's unlikely survival bid with 21 points and all but ends Warwickshire's hopes of stealing the Championship crown from an increasingly dominant Yorkshire.
Edwards has now taken 22 wickets in four Championship matches at 21.45 and has bowled some of the fastest spells of the season, making him a key figure in Hampshire's attempt to escape demotion.
Jackson Bird has announced he is returning to his Australian state side Tasmania at the end of the month to be replaced by South African all-rounder Ryan McLaren.
Rikki Clarke provided solid resistance on the third day with a stoic 53, but he appeared in a rush in the morning flicking the first ball through the leg side for two. Atempting to repeat the shot to the fourth ball of the day he loosely chipped to Joe Gatting at mid-wicket off Bird.
Edwards added his eighth wicket of the match by having Keith Barker lbw in the second over of the morning - as Warwickshire capitulated before the forecast rain.
Chris Woakes provided a luscious cover drive and a clip off the hips for boundaries as he offered a selection of good looking shots for the sparse crowd.
Jeetan Patel got away with an edge to slip which did not quite carry to Liam Dawson at second slip. Then in the next over a vicious bouncer from Edwards saw off the New Zealander, as the ball looped off his glove to Will Smith at short leg.
Woakes and Boyd Rankin frustrated the home side with a 41-run partnership in 86 balls as Hampshire were only allowed to utilise spin in dreary conditions.
Smith finally broke the partnership nearly 90 minutes into the morning as Woakes clipped to Mason Crane at mid-on - to give Hampshire a 216 run win.