England seamer James Anderson, who took 3-5 on the third evening, finished with figures of 4-20 as the Red Rose skittled Hampshire for 168 on day four.
The visitors had resumed on 50-5, still trailing by 148, and were unable to make Lancashire bat again.
Dane Vilas' 244 had put the home team in control earlier in the match.
Alex Davies and Ryan McLaren also chipped in with centuries to give Lancashire a big first-innings lead, but it was their impressive bowling display in Hampshire's second innings that ensured victory.
Anderson's 15 overs cost only 20 runs as he tore through the visitors' top order, while McLaren (3-41) and Kyle Jarvis (3-49) did the rest of the damage.
England's all-time leading wicket-taker Anderson was playing in his first match after a month out through injury, with his country's first Test of the summer against South Africa starting on 6 July.
Gareth Berg, the last Hampshire wicket to fall, top-scored with 49, while James Vince's 29 was the next best individual effort.
Lancashire have gone above Hampshire and Yorkshire up to second in Division One, 14 points behind leaders Essex, who beat Warwickshire - also by an innings.
England fast bowler James Anderson told BBC Radio Lancashire:
"Not many people would have expected Essex and Lancashire to be first and second after seven games but we're in a really strong position and we have a lot of competition for places.
"We're not going to get carried away. We now have a big game against Warwickshire and, if we get a result there, it will put us in a great position before the back end of the summer.
"We're better placed to sustain this position but we have to make sure that what happened last year doesn't happen again. This week was a really good performance but there are still areas on which we can improve.
"Al Davies, Dane Vilas and Ryan McLaren got us up to a really good score. Dane and Ryan are really solid professionals who have been fantastic additions. And we thought if we could put the ball in the right areas we could really challenge them and take 10 wickets."
Hampshire coach Craig White told BBC Radio Solent:
"It was going to be a big ask. But to fold again on a pretty good pitch is extremely disappointing.
"Bergy tried and there was a bit of fight there at the end, but it was too much to ask really.
"Anderson bowled beautifully, but the ball's allowed to swing and we should be able to combat that.
"It seems that if the ball does swing or seam we get in a bit of trouble. We need to work on that, improve on that, try and stay positive, and get back on the horse, so to speak."
Lancashire moved up to second in the County Championship table after thrashing Hampshire by an innings and 30 runs at Old Trafford.