Anderson set aside any concerns over the disciplinary proceedings he must face on Friday morning, over his spat with Ravindra Jadeja in the first Test at Trent Bridge, to provide England with the early impetus in the final strait here.
The linchpin seamer finished with match figures of seven for 77, after taking the first two of six wickets England still needed to make it 1-1 with two to play.
Anderson may well be absent, depending on the outcome of his Level 3 charge, when these two teams rejoin battle on his home ground at Emirates Old Trafford next week.
Moeen (six for 67) surely will be in action in Manchester, though, increasingly belying his billing as a mere part-time off-spinner after taking his series tally to 15 victims and counting, and match haul to eight with his maiden five-wicket return here.
Only Ajinkya Rahane's defiant and unbeaten 52 held England up for long, after India resumed on 112 for four still in notional pursuit of a world-record 445 but were bowled out before lunch for 178.
Anderson had England up and running with only his third delivery, Rohit Sharma apparently surprised to be given out caught-behind pushing forward at a delivery he might perhaps have left.
He had to go, though, without addition to his overnight six - and India did not reopen their account either until well into the fourth over of another sunny morning.
There was no doubt about Anderson's next success, another caught-behind and Jos Buttler's sixth on debut, when Mahendra Singh Dhoni got a much more obvious edge on some full-length swing to also go for six.
Given their recent history, and impending hearings, new batsman Jadeja was surely also on Anderson's hit-list.
But having got both Dhoni and the left-hander among his five first-innings victims, Anderson could not double up this time.
Instead, after a 13-over wait for England, it was Moeen who got Jadeja - yorking himself as the off-spinner drifting one into him to hit the bottom of off-stump.
For good measure, Mooen then saw off Bhuvneshwar Kumar - so often England's stumbling block in the India tail this summer - for a duck, his second wicket in the same over, with an inside-edge on to his pad and into the hands of gully.
Moeen then made short work of Mohammed Shami, clean-bowling him and soon afterwards number 11 Pankaj Singh to end the match.
The only shame was that, although a much bigger crowd than expected was in attendance to cheer Alastair Cook's team to their first win in 11 Tests - dating back to last summer's Ashes - some arrived barely in time to see the tourists' terminal falter.
Park-and-ride arrangements at this out-of-town venue did not extend until the last day of the match, and demand turned out to be high to witness the culmination of England's mid-series resurgence.
In the end, though, India lasted long enough to ensure almost everyone arrived in time for the end of England's party.
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- Ravindra Jadeja