The Argentinian, whose differences with the club have been resolved, put the Magpies to the sword in a blistering opening to the game, setting up Gareth Barry's opener with just 72 seconds gone and then helping himself to a second in the fifth minute.
Then after Andy Carroll had dragged Alan Pardew's men back into the game with a 72nd-minute header, his 11th goal of the season, Tevez ended Newcastle's hopes when his 81st-minute effort ended up in the back of the net with the help of two deflections.
The result was the perfect antidote to Monday night's 2-1 home defeat to Everton, although City were made to fight all the way by a Magpies side which, having seemingly thrown the points away barely before they had broken sweat, threatened to emerge with something to show for their efforts in front of a crowd of 51,635.
By contrast, the Magpies were left to reflect on a fourth home league defeat of the season and looking anxiously over their shoulders ahead of Tuesday's difficult trip to Tottenham.
Despite having tasted victory over Liverpool in his only game to date at the helm, Pardew went into this afternoon's encounter knowing the degree of difficulty to be significantly higher, and a cursory glance at the team-sheet would have illustrated the gulf between a club which is now being run on a strict budget and the richest in world football.
Opposite number Roberto Mancini was even able to leave £24million signing Mario Balotelli sitting on the bench after serving the 20-year-old with a reminder as to what is expected of him.
But where Newcastle could not compete in terms of quality, they would have backed themselves to do so when it came to passion and honest endeavour.
In the event, their game plan was torn up inside five disastrous minutes when they twice pushed the self-destruct button to hand the advantage to the visitors.
Keeper Tim Krul has proved an able deputy for Steve Harper during his spell on the sidelines with a shoulder injury, but his ill-judged second-minute pass to Joey Barton handed the midfielder's former club the perfect opportunity to get their noses in front.
Tevez anticipated well to steal possession and slide a pass into the run of Barry, who dispatched it past Krul into the bottom corner.
Worse was to follow barely three minutes later when the Argentinian picked out former Magpie James Milner on the right and then found space between central defenders Fabricio Coloccini and Steven Taylor to meet his cross and guide it expertly into the top corner.
Tevez was simply too hot to handle as he repeatedly dropped deep to find space before running at the heart of the home defence as they back-pedalled in sheer terror.
However, lone striker Carroll perhaps should have dragged Newcastle back into the game when he headed a sixth-minute Wayne Routledge cross straight at keeper Joe Hart, and having survived further damage, Pardew's men started to work their way back into the game.
Carroll proved a major handful for central defenders Vincent Kompany and Joleon Lescott, and Hart had to collect his 31st-minute looping header and was then grateful to see his diving injury-time effort fly wide.
But in the meantime, full-back Aleksandar Kolarov had blasted two long-range efforts just over to remind the home side of City's potency from all areas.
Carroll sent an acrobatic 59th-minute volley wide from Jonas Gutierrez's cross, and Pardew made his move seconds later when he sent on striker Nile Ranger for Routledge and adopted a 4-4-2 formation.
City were content to try to hit the Magpies on the break and Yaya Toure embarked upon an enterprising 63-minute run which was only ended by Coloccini's desperate challenge deep inside his own penalty area.
Gutierrez sent a looping header across the face of goal six minutes later, but Newcastle got their break three minutes later when Carroll powered home a header from Barton's crooner.
Hart protested with some justification that he had been blocked by Kevin Nolan, and was booked for his pains as the home fans settled in for a grandstand finish.
With Barton and Cheik Tiote snapping at heels and Carroll in menacing form, the Magpies looked the more likely scorers, but their hopes were dashed in unfortunate fashion with nine minutes remaining.
Jose Enrique and Coloccini looked to have got back to close down Tevez, but his shot deflected off both of them to wrong-foot Krul and creep inside the post.
There was still time for substitute Balotelli to be booked for a foul on Tiote, but that was off little consequence to the home side.