The Argentinian, making his second start since returning to the City fold, also set up the first of compatriot Sergio Aguero's double in the rout with a neat backheel.
Winger Adam Johnson added a sixth late on as City moved within two points of United, who face Aston Villa in their game in hand on Sunday.
Norwich struck through Andrew Surman to make the score 2-1 early in the second half but it proved no more than consolation as City, and Tevez in particular, got back to their best.
Blackburn remained in the bottom three as they slumped to a 3-0 defeat at Swansea, who passed the 40-point mark in the process.
Gylfi Sigurdsson curled in a superb opening goal for the Swans after 37 minutes and Nathan Dyer took advantage of poor defending to double the advantage just before the break.
Swansea's third came just after the hour as the ball rebounded in off Scott Dann after Sigurdsson hit the post following good work by Scott Sinclair.
The closest Blackburn, who have now lost five in succession, came was when David Dunn hit the woodwork with a curling effort.
QPR missed a chance to pull away from the relegation zone as they were beaten by a stunning strike from Graham Dorrans at West Brom.
Dorrans scored the only goal of the game at The Hawthorns when he blasted in from 35 yards after 22 minutes.
Rangers had a number of chances to equalise, with Bobby Zamora going close three times and Jamie Mackie shooting narrowly wide, but Billy Jones also hit the post for Albion.
The day's other game between bottom side Wolves and Sunderland at the Stadium of Light proved an uneventful affair which ended goalless.
Terry Connor's Wolves are now eight points off the safety of 17th place with just four games remaining.
Saturday's Premier League Results
Norwich 1-6 Manchester City
Sunderland 0-0 Wolves
Swansea 3-0 Blackburn
West Brom 1-0 QPR
Sunday's Premier League Fixture
Monday's Premier League Fixture