The off-spinning all-rounder rose to the occasion on the final day at the Ageas Bowl on Thursday, taking 6-67 as India were all out for 178 in a 266-run triumph for the hosts.
England dominated all five days in Southampton to end their run of 10 Tests with a win and Moeen stressed the importance of building on that platform ahead of the fourth meeting at Old Trafford next week, with the five-match series level at 1-1.
He told the ECB website: "I think we've set our standard now,
"That's the level of cricket we want to play - to really boss the game as much as we can, every session counts. Hopefully that's a kick-start into a new era."
Moeen's ability to cut it as a spinner in Test cricket had been called into question, but his first five-wicket haul in the longest format of the game should go a long way to dispelling the doubters' scepticism.
And the Worcestershire man was delighted to play his part in a victory that eased the pressure on captain Alastair Cook.
He said: "I'm just very happy. I’m more happy that I contributed to the team winning the game.
"That makes me more happy, but even if I didn't and we won the game I'd still be really happy."