Warwicks declared on 630-8 and left Hampshire needing 251 to avoid defeat.
Micheal Lumb made 84 and Nic Pothas 65 as Hants made 301-6 to earn a draw. Ant Botha took four wickets and Boyd Rankin the other two in a match which saw Warwicks earn 12 points compared to Hants nine.
Warwicks next County Championship game is against Yorkshire at Edgbaston starting on May 6th.