The Manchester City striker celebrated his first goal with a gesture that appeared to hit back at comments from the United skipper, who claimed this week that the club had been right to sell Tevez to their rivals.
Neville, who was warming up on the touchline, flashed back an offensive one-fingered response which could land him in trouble with the FA.
Unhappy Tuesdays: After netting the equaliser, Carlos Tevez signals at Gary Neville, who responds with an obscene gesture of his own
After giving City a 2-1 lead to take to Old Trafford in next Wednesday night's second leg, the Argentina forward said: 'This was special for me. My two goals were for the City fans.'
Ryan Giggs had given United the lead by tapping in after City goalkeeper Shay Given had kept out Wayne Rooney's shot. It was Giggs' first derby goal since 1996.
VIDEO: Watch Roberto Mancini's reaction to Manchester City's victory over rivals UnitedBut Tevez equalised with a penalty after Rafael da Silva tugged Craig Bellamy'sshirt and then tormented his former club with the sweetest of headers in the second half.
He then ran towards the dug-out and cupped his ears in a celebration reminiscentof his demonstration towards the United board after scoring against City at Old Trafford last season.
Net pains: Tevez blasts his penalty past Edwin van der Sar
City midfielder Gareth Barry hailed Tevez's display but insisted the tie was far from over.
He said: 'All the talk before the game was about Carlos but he did his talking on the pitch, as he always does, with a great performance. The tie is still in the balance and we expect a real battle at Old Trafford. Shay Given pulled off some great saves but it was a good all-round performance.'
United manager Sir Alex Ferguson had no regrets about letting Tevez leave. He said: 'We've had a few players who have left the club and scored against us. It is not an issue. For most of the game we were in control but those mad two minutes beforehalf-time brought City back into the game.'
Ferguson was clearly unhappy at referee Mike Dean's decision to award City a penalty amid suggestions Rafael had fouled Bellamy outside the box.
'I'm not getting into the penalty,' he said. 'Everyone could see it for themselves. The decisions have gone against us.
'But the crowd will make a difference at United and if we perform like we did tonight, we will be okay.'
High praise: Tevez is congratulated by his manager Roberto Mancini after scoring the winning goal
City manager Roberto Mancini punched the air after watching his side take a step nearer their first trophy for 34 years.
The Italian said: 'I'm very happy for Carlos because it was important for him to score two goals against United. I don't know the situation with Gary Neville but I hope Carlos can play as well in the second game and score another goal. I don't know if there is a better striker in the Premier League at the moment.'
Mancini refused to believe City had one foot in a Wembley final and added: 'We have an advantage now, a 51 per cent chance of going through. We know we will have a hard game at Old Trafford.'
City could also be in trouble with the FA after Patrice Evra was hit by a lighter as he went to collect the ball for a throw-in in the second half.
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