Opting to bat after winning a crucial toss, Joe Root's men once again looked clueless against the in-form spin combination of Patel and Ravichandran Ashwin.
The visitors lost four wickets in the opening session before unravelling completely in the second.
While Patel picked up for 6/38 in 21.4 overs, Ashwin returned figures of 3/26.
Veteran pacer Ishant Sharma, who is playing in his 100th Test, also chipped in with one wicket.
Opener Zak Crawley was England's top scorer with a breezy 53-run knock that came off 84 balls before he was trapped LBW by Patel. Crawley's impressive stay at crease included 10 fours.
Skipper Joe Root's 17 was the only other notable contribution in the below-par total.
The series is currently tied 1-1 after England triumphed in the opener and India claimed the honours in the second game.
England 1st Innings: 112 all out in 48.4 overs (Zak Crawley 53, Joe Root 17, Axar Patel 6/38, Ravichandran Ashwin 3/26, Ishant Sharma 1/26).