The visitors made just 139 in their second innings, but Ali spun his side to victory as the hosts were dismissed for just 63 in their second innings - their lowest total at Old Trafford since 1963 - with Gareth Cross the only batsman to reach double figures.
At Arundel, Durham lead Sussex by 80 runs with three second innings wickets and one day remaining after Steve Magoffin took four for 14 in 10 overs to leave the visitors in trouble at 80 for seven.
The hosts could add just 131 runs from their overnight total of 100 for three, with Callum Thorp and Chris Rushworth picking up four wickets apiece.
Paul Collingwood is seemingly Durham's last hope of a decent total and is unbeaten on 29.
Warwickshire are firmly in control of their clash with Somerset at Taunton after bowling the hosts out for 254 - 146 runs shy of the visitors first innings effort with Jeetan Patel taking seven for 75.
Ashley Giles' side ended day three on 66 for three to extend their advantage to 212.
Arul Suppiah made 54 for the hosts, while Nick Compton ended the innings unbeaten on 73, with those around him struggling as Craig Kieswetter (44) was the only other batsman to go beyond 20.
Ramnaresh Sarwan (50) was the only man to register a half century for the visitors, who compiled 162 in their first innings as Ian Saxelby captured the last four wickets without conceding any runs to finish with impressive figures of six for 48.
In reply a 95 run partnership between Ed Young (37) and James Fuller (57) pushed the hosts to 229 all out, as Nathan Buck and Wayne White took three wickets apiece.
Leicestershire forged a slender 75-run lead with five second innings wickets remaining after an eventful day against Gloucestershire at Cheltenham in the LV= County Championship Division Two.
Leicestershire rallied in the second innings to end the day 142 for five.
Kent were not given much of an opportunity to build on their positive performance on day two of their match with Glamorgan at Canterbury thanks to the weather.
Centurions Brendan Nash (114) and Darren Stevens (123) could add only seven runs to their overnight totals before departing. Geraint Jones hit a quick fire 69 for the hosts as they ended the day 456 for nine.
Essex's Division Two clash with Hampshire was called off for a second day after heavy rain throughout the morning, with the visitors remaining 303 for six.
There was no play between Derbyshire and Yorkshire for the second day running with the hosts on 135 for seven, 84 runs behind the visitors.
The game at Trent Bridge suffered a similar fate as no play was possible with Nottinghamshire still 178 for five in their first innings against Surrey.