Adams made 149 before departing with only 49 required as Hampshire eased to their fourth win of the season to maintain their strengthening promotion challenge.
The opener hit 23 fours and two sixes from 216 balls and after his departure, Simon Katich's unbeaten 61 made sure of Hampshire's victory.
Yorkshire had to settle for a draw at Headingley after a pulsating first half-hour's play had seen table-topping Derbyshire follow-on 152 runs adrift on the final day.
Derbyshire then lost two quick wickets to Tim Bresnan to put Yorkshire on course for victory but Usman Khawaja led a spirited fightback in the last two sessions with a sparkling unbeaten 110 and the visitors reached 190 for five, 38 ahead, to bring about the stalemate.
Jim Allenby's first hundred of the summer and a fighting half-century by Ben Wright ensured that Glamorgan earned a draw from their clash with Essex at Colchester.
The encounter ended with the Welsh county on 260 for six in their second innings, an overall lead of 178, as both sides were forced to settle for a share of the spoils.
Gloucestershire's weather-affected game against Kent at Bristol petered out into a draw - but ironically finished in blazing sunshine.
The visitors finished the fourth day on 300 for nine declared before the hosts opted to declare their own first innings with just one run on the board.
It was an unsatisfactory conclusion for both sides, who finished with six points each.