Tevez's treble helped City reach the FA Cup semi-finals after a 5-0 thrashing of Barnsley on Saturday and it came just two days after the Argentinian was arrested on suspicion of driving whilst disqualified.
The 29-year-old's ability to put aside off-field issues was not a surprise to Lescott, with Tevez having been embroiled in a lengthy dispute with City last season before playing a key role in the club's Premier League title success.
He said: "His performance doesn't surprise me, to be honest. He has been our most consistent player since I joined the club.
"In his first two years he carried the team on his back. We won a lot of games by one goal, and that was down to Carlos - when he plays like that he is unplayable."
Lescott is hoping City can now go on to repeat their 2011 FA Cup success after being fired up for the Barnsley game by Everton's shock defeat by Wigan earlier in the day.
"We knew it would be tough, but we had all watched the game earlier," said the former Everton defender. "Everyone predicted an Everton win, but Wigan surprised most people.
"We didn't want that to happen to us so we had to put in a professional performance.
"The manager set our stall out before we even travelled to the stadium, saying that if we were professional and played in the right way it would be hard for Barnsley to create many chances. From the get-go we proved that, and made it hard.
"Now we are at the business end of the competition and it's not about keeping clean sheets but winning games. We need to win the next two, and we have our name on the cup again."