Tevez's Argentina team-mate Sergio Aguero weighed in with a couple of goals of his own while substitute Adam Johnson scored in injury time as Roberto Mancini's side closed the gap on leaders Manchester United to two points.
United have played one match less with City having four fixtures left to overtake their foes. It makes for brighter reading for a City team who were eight points adrift after a 1-0 defeat at Arsenal last Sunday and apparently destined to finish second.
City's previous 6-1 win this season came against United at Old Trafford in October.
The manner of this win over Paul Lambert's men at Carrow Road was every bit as impressive as the powers of recovery they displayed to sink QPR 3-2 on November 5 in London.
Sir Alex Ferguson's side remain in the driving seat to claim their 20th English title if they complete wins over Aston Villa, Everton and Manchester City in their next three matches, but their 1-0 loss at Wigan in midweek has given City fresh impetus.
At least this triumph keeps alive their hopes of a first title since 1968. With their goal difference now eight better than United's, things could yet get tighter at the top with Villa visiting Old Trafford on Sunday.
Tevez responded to taunts of "he wants to go home" by the Norwich fans by rattling in a venomous shot that swerved in the air from 25 yards out to leave home goalkeeper John Ruddy with no chance on 18 minutes.
Tevez - who supplied David Silva to see a shot blocked by Ruddy on five minutes - had been unfortunate to be booked for diving by referee Chris Foy on 10 minutes when television replays showed he had been clearly caught on the top of a boot by Ryan Bennett in the box. Bennett was subjected to a nightmarish sort of afternoon, but few men in the home team earned passmarks.
Tevez continued to revel in his surroundings as he played provider with a lovely backheel for Aguero to thump a volley beyond Ruddy from outside of the home box on 27 minutes.
Norwich's best moments of the first period came courtesy of Grant Holt, who saw a header nodded off the line by Joleon Lescott and a volley held by England goalkeeper Joe Hart.
In truth, they ended the first half a distant second to the visiting side and the pattern continued in the second period despite a brief rally when substitute Andrew Surman hooked a loose ball home on 51 minutes after Hart had failed to punch a cross out of his area.
Tevez restored his side's two-goal advantage as he netted his second goal of the game when he out-jumped Ryan Bennett to nod into the net on 73 minutes after Ruddy had halted Yaya Toure's shot.
Aguero then planted a wonderful swerving effort beyond Ruddy on 75 minutes for City's fourth before Tevez rounded the exposed goalkeeper for his hat-trick after Bennett was short with an attempted passback.
Tevez celebrated by swinging an imaginary golf club - poking fun at his absence from the team for several months after his well-publicised public fall-out with Mancini during a Champions League match at Bayern Munich - but City were not yet finished.
Johnson finished from close range from Gael Clichy's pass in injury time after a lovely ball across goal by Aguero, who like Johnson had seen a shot come back off a post with Norwich clearly desperate to get off the park.