Starting successive Premier League games for the first time in 11 months, Tevez blasted home a 20-yard swirling shot to open the scoring at Carrow Road on Saturday 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 famously went AWOL in Argentina for four months after refusing to warm up 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 lead ahead of their game against Aston Villa tomorrow, and the Manchester derby on April 30 looks an even more appetising prospect after Tevez's fine display today.
The Argentinean played a big part in City's 4-0 annihilation of West Brom in midweek and it was clear from the start today that the win had clearly raised confidence levels at the Etihad Stadium.
The warning signs of a drubbing were there from the kick-off.
David Silva chipped the Norwich defence looking for Samir Nasri but his touch let him down and John Ruddy came to the rescue.
Norwich hit back on the counter through Anthony Pilkington, who skipped past Pablo Zabaleta and embarrassed Nasri with a clever turn but he curled wide from 10 yards.
Play continued to fly from end to end and Tevez looked a big threat for the visitors.
Ruddy saved well from the Argentina striker before he then went down under a challenge from Ryan Bennett.
The defender clearly caught Tevez's standing leg but Chris Foy flashed a yellow card for diving instead of awarding a penalty.
City were furiously denied another penalty moments later when Pilkington tugged Aguero's shirt but Foy again gave no penalty.
Grant Holt met a looping ball in the box but Joleon Lescott cleared the striker's header under the bar.
After an entertaining spell it seemed inevitable an opener would come and it did in the 18th minute.
Elliott Ward's short pass allowed Silva to find Tevez via Aguero and the former Manchester United man unleashed a 25-yard swerving shot that beat Ruddy at his near post.
Nine minutes later it was 2-0. Tevez and Aguero exchanged passes twice on the break, the second of which was a clever backheel, and Aguero volleyed home from 20 yards.
Norwich went in at half-time firmly on the back foot and the home crowd feared a rout.
The last time City visited Carrow Road in 2005, Canaries owner Delia Smith took to the pitch at half-time to give her toe-curling "let's be havin' you" address to the Norwich faithful.
Thankfully she refrained from doing so today, and whatever Paul Lambert said instead inside the confines of the dressing room worked briefly as Norwich pulled one back through Surman.
The substitute collected the ball from Hart's punch before rifling a 20-yard screamer in to the net.
The goal boosted Norwich, but City held strong.
Tevez broke clear only to be hauled back by Ryan Bennett with a tackle that would not look out of place on a rugby league pitch. The defender rightly entered the referee's book.
Ruddy saved from Pablo Zabaleta with his legs as City looked to restore their two-goal cushion.
Norwich's resistance was broken again in the 73rd minute thanks to Tevez's second.
Ruddy blocked Yaya Toure's powerful drive, the ball flew up in the air, and Tevez beat his marker to nod home in to an empty net.
Less than 90 seconds later City were 4-1 up. This time it was Tevez's compatriot Aguero who struck, curling a wonderful 20-yard effort beyond the out-stretched Ruddy.
Tevez's remarkable afternoon was completed with 10 minutes to go when he beat the offside trip and rounded Ruddy before mimicking a golf-swing in his celebration in front of the travelling fans.
Whether the celebration was a dig at Mancini, who lambasted Tevez for spending his time playing golf while in exile earlier this season or not he was replaced seconds later for Richards.
Johnson, who had earlier come on for Silva, struck the bar in the final minute and Aguero did the same in injury time.
Aguero found Clichy at the back post in the 93rd minute, he squared to Johnson and he made no mistake from six yards to complete the pummelling.