Starting successive Premier League games for the first time in 11 months, Tevez blasted home a 20-yard swirling shot to open the scoring before he backheeled to Sergio Aguero, who made it 2-0 with a venomous volley.
Andrew Surman pulled one back just after the break to give the Canaries hope, but a Tevez second-half double, a late strike from Adam Johnson, and a majestic curler from Aguero gave City a hugely impressive victory to cut United's lead to two points.
Tevez, who went AWOL in Argentina for six months after refusing to come off the bench against Bayern Munich, is now well and truly back to his best and could yet have a decisive say in this title race with his former employers.
The diminutive striker looked sharp all afternoon, dropping deep and working the channels all game to cause the Canaries all sorts of problems, and his finishing was quite superb.
Having pegged United back to a five-point lead in midweek, the Red Devils now only have a marginal two-point lead ahead of their game against Aston Villa, and the Manchester derby on April 30 looks an even more appetising prospect after Tevez's fine display.
The Argentinean played a big part in City's 4-0 annihilation of West Brom in midweek.