The hosts began the final day on 280 for nine in their second innings, leading by only 68, and added 19 runs in 25 minutes before being bowled out for 299, Jack Taylor last man out for 48.
That left Northamptonshire requiring 88 to win and, despite some spirited Gloucestershire bowling, which accounted for Kyle Coetzer, Stephen Peters and Alex Wakely, they reached 90 for three off 22.3 overs just before lunch.
Hampshire grabbed their first championship win since mid-August by thumping an out-of-sorts Worcestershire by an innings and 42 runs at the Ageas Bowl.
Resuming on 159 for five and faced with the unlikely task of batting all day to save the game, Worcestershire's second innings yielded 252.
Lancashire declared on 395 for seven against Kent in Manchester, with the visitors reaching lunch on 29 for one - trailing by 122.