Australia leg-spinner Warne, the Hampshire captain, played a key role in kick-starting a Middlesex collapse as the visitors lost three wickets for as many runs on the fourth and final afternoon in their pursuit of a testing 301.
Pace bowler Chris Tremlett, recently called up to England's development squad, was also in form with four for 59 as Hampshire ended the day third in the table.
Leaders Nottinghamshire, who have a similar record to Hampshire and second-placed Warwickshire, stayed ahead on bonus points, after a crushing innings and 71-run win against Surrey at The Oval.
Not even a combination of a century from ex-England batsman Mark Ramprakash (107) and London rain could prevent Surrey being bowled out for 404 in their second innings.
Gloucestershire, resuming on 59 for three, easily got the 60 runs they needed for a seven-wicket win away to western rivals Glamorgan to complete a maximum 22-point victory.
Defeat meant Glamorgan has lost all three of their opening championship matches.
In the Second Division, Durham made it three wins from three with a four-wicket success against Somerset at Stockton.
Andy Caddick did his best to keep Somerset in the game with the former England quick bowler scoring before taking six for 98 for match figures of 12 for 204.
But hosts Durham overcame Caddick's one-man show to reach 244 for six.
At Chelmsford, former Zimbabwe captain Andy Flower scored an unbeaten 74 as Essex, chasing 191, beat Leicestershire by six wickets.
Elsewehere left-armer Gary Keedy proved there was more to Lancashire spin bowling than Muttian Muralitharan by taking six for 60 in the innings and 72-run defeat of Derbyshire at Old Trafford.
Yorkshire made sure the weather couldn't halt their victory pursuit against Northamptonshire at Headingley by sprinting to a 10-wicket win.
The hosts needed only 20 overs to reach their target of 129 with Australian Phil Jaques 70 not out and Matthew Wood 56 not out.