The Bears batted first and were grateful to Jon Trott who top scored with ninety, hitting six fours out of the ten hit by Warwickshire players.
Only four players made double figures including Trott and Van Jaarsveld in a total of 196-8.
This was an easy target for Hants who lost the wickets of Lumb (82) and Crawley (14) to the bowling of Jimmy Anyon.
Ervine hit eighty and the winning runs were hit by Michael Carberry to give Hants a win by eight wickets with more than ten overs to spare.