Wolves boss Mick McCarthy was left cursing the "little Argentinian with great feet" for ensuring Manchester City went top of the Barclays Premier League.
McCarthy's team could not have done much more in an outstanding opening half-hour at Eastlands.
But their failure to build on Nenad Milijas' opener left them vulnerable, and once Tevez had put City ahead with a superb effort just after the interval, the Blues always had their noses in front, even if a late Wolves rally made for a tense period of stoppage-time before they were able to claim a 4-3 win.
"Tevez got a lucky ricochet and the ball fell in his path," said McCarthy. "After that it was a brilliant goal. I know everyone wants me to criticise defenders. But he runs at you, he gets in the box, he has quick feet. At some stage you have to say it was a great goal.
"I thought we played really well. But we lost because they have that little Argentinian with great feet who has waltzed through our back four."
Little wonder McCarthy was so frustrated.
Had Aleksander Kolarov not blocked Matt Jarvis' goalbound effort, or Wolves stayed in front until the break, they might well have completed an unlikely double over the Premier League's big spenders.
As it was, Kolo Toure levelled just before half-time, then Tevez skipped between defenders and cut inside Richard Stearman before calmly putting his side ahead.
Yaya Toure added another before Tevez joined Dimitar Berbatov at the top of the Premier League scoring charts with his 14th of the season.
Still Wolves would not be denied. Kevin Doyle scored a penalty before Ronald Zubar added another to set up a tense finale.
"Forget the disparity between resources," said McCarthy. "I am disappointed we have lost.
"But most teams would have laid down and had their backsides slapped at 4-1 down. It just shows what spirit the lads have got.
"There were a few squeaky bums when five minutes' injury-time went up. I was getting a lot of abuse at 4-1. At 4-3 with five extra minutes I thought they had all left."
In the end though, it was City celebrating top spot as Wolves slid back into the bottom three.
"I am very happy for Carlos. He played very well and the first goal he scored was fantastic," said Blues boss Roberto Mancini, who was also impressed with £27million debutant Edin Dzeko.
"It is his first game for 30 days and his first game for a new team.
"He played well but he needs to work. He showed he is a good player."
He also showed he was prepared to graft and act as support to Tevez if required, although - as Mancini acknowledged - there is still work to do, for them as well as his team.
"It is their first game and they have only worked together for one week," said Mancini.
"Dzeko needs three or four games to work with his team-mates and know the team well.
"It is not easy at the moment but Dzeko is a good player and so is Carlos. When you have two good players, it is easy to play together.
"Overall, we must improve.
"When you are 4-1 up after 75 minutes, you should control the game better, not think it is finished. In England the game is never finished."
