In a match, shown live by Sky, Hampshire batted first at Edgbaston and were allowed to go on a run fest.
Jimmy Adams hit 131 runs from only 104 balls including nine fours and four sixes with Michael Carberry hitting 103 from seventy balls.
Sean Ervine added 48 before he was stumped by Tim Ambrose as Hants ended their forty overs on 341-6.
It was a score that always looked tough to be beat and when Neil Carter went for 20. Things did not look good but Ian Bell and Jon Trott started to hit runs. The Coventry born batsman had made 41 before he gave his wicket away with a catch to Michael Carberry.
Jim Troughton was well caught by Herath and when Darren Maddy was stumped, Warwicks were getting themselves in trouble.
Ian Westwood made 18 and Keith Barker 26 as Warwicks went down to an innings and 130 run defeat.
Warwickshire travel to Taunton on Monday for a County Championship game.
Ball by ball coverage is available on the BBC Coventry & Warwickshire website.