Left-arm spinner Simon Kerrigan took 5-59 as the visitors were bowled out for 253 to lose by an innings and 94 runs.
Adam Wheater (47) and Will Smith (45) resisted but after Wheater fell, the last five wickets fell for 45 runs.
Lancashire have won two of their opening three Championship matches - the same amount of the rest of the top flight put together.
This success was largely built on dismissing Hampshire for 109 on the first day, but their push was halted by the loss of two sessions to the weather on day three.
On an overcast but uninterrupted final day, the home side were forced to work hard for the eight wickets they required in conditions that offered little to the pace bowlers and on a batting surface that remained true.
Resuming on 76-2, 271 behind, Hampshire lost England hopeful James Vince for the addition of eight to his overnight 39, driving to short cover to give James Anderson a third wicket.
It could have been argued that Hampshire's best chance of saving the game went with their captain, but the obdurate Smith ate up 213 deliveries before being trapped in front by Kyle Jarvis.
Wheater, strong off the back foot, once again batted well, only to be pinned leg before by a quicker one from Kerrigan.
From there Kerrigan, giving the ball more air to find increasing amounts of turn, worked through the lower order with the help of leg-spinner Liam Livingstone, who had Tino Best lbw for his maiden first-class wicket.
Kerrigan completed his 12th five-wicket haul and the match when Mason Crane top-edged a sweep to leg slip.
Hampshire captain James Vince told BBC Radio Solent:
"The morning of day one we put ourselves on the back foot and it was always going to be difficult to claw ourselves back into that game.
"We showed some glimpses of good cricket, but again we haven't strung it together. To get off to a start like that, it was always going to be incredibly tough to turn it round.
"A disappointing result and a disappointing first day especially. But, there are still signs there that we are playing some good cricket and some guys are in good form."
Lancashire completed victory over Hampshire to move into second place in County Championship Division One.