They began the final day needing a further 134 with nine wickets intact.
Dimitri Mascarenhas struck twice in two balls for Hants before Mark Wagh reached fifty from 57 balls, but with only 70 more needed rain intervened.
That prompted an early lunch and tea, but 40 overs were left as play resumed and though Wagh fell for 67, Samit Patel hit 11 fours in an unbeaten 65.
Hampshire’s faint hopes of victory were not helped by an injury to paceman Nantie Hayward, that prevented the South African taking the field.
But Mascarenhas induced Will Jefferson to edge a simple catch to Michael Lumb at slip for 21 and when Adam Voges gave a bat-pad catch to wicketkeeper Nic Pothas it was 74-3. and 114 were still required.
England pace bowler Chris Tremlett failed to find line and length, however, and conceded 27 from his first four overs.
Wagh and Patel put on 91 in 18 overs for the fourth wicket, but with only 23 more needed Wagh flashed at a wide delivery from James Tomlinson to give Pothas another catch.
Patel edged an outswinger from James Tomlinson but Sean Ervine put down a routine chance at second slip, and the burly Notts all-rounder struck the winning runs with a fluent stroke to the mid-wicket boundary.