Surrey added twenty nine to their overnight score,leaving them 58 runs ahead of Warwicks who were all out in their second innings for 268.
Ian Westwood top scored with 79 whilst Jim Troughton added 43 and Jon Trott 33.
Needing 184 to win,Surrey were 2-0 at the close.
In the deciding One Day International at Lords, England trounced India by seven wickets.
Andrew Flintoff took 3-45 as India were pegged back to 187 in their fifty overs.
England lost Prior and Luke Wright without scoring but Coventrian Ian Bell came in and hit 36 before being run out. Kevin Pietersen (71) and Paul Collingwood (64) saw England past the total to record a series victory.