The Argentine was instrumental in the champions' 2-1 victory over their rivals at Old Trafford, in a match that saw Sergio Aguero score the winner after an unfortunate Vincent Kompany own goal had cancelled out James Milner's opener.
However, Savage believes that Tevez deserves mass plaudits for his performance and the way he brought his teammates into the game.
"City's lineup, with only one recognised striker in a 4-2-3-1 formation, did not look that attacking at first, but Tevez helped them take control of the game with his play in United's half," Savage told BBC Sport. "He kept dropping deep to collect the ball and, every time it went into him, he held it up.
"His first touch was fantastic and he brought the three players immediately behind him - James Milner, Samir Nasri and David Silva - into the game, and in dangerous positions in the United half too - often in their area. That trio were industrious and effective, particularly Milner, who seems to be something of an unsung hero for City. His play down the right when he linked up with Pablo Zabaleta was again superb.
"The front four players of Tevez, Milner, Nasri and Silva took the game to United, and Sergio Aguero continued that when he came on for Nasri and replaced Tevez as City's most advanced forward player, seeing plenty of the ball in and around the United box before he scored City's winner."
City have now closed the gap at the top of the Premier League to 12 points.