Manchester United led through Ryan Giggs' 17th-minute tap-in but City drew level after Rafael was adjudged to have hauled back Craig Bellamy inside the box.
Tevez gleefully rammed home the penalty, then turned home Vincent Kompany's cross from close range after the interval.
In a pulsating encounter at Eastlands, United pushed forward frantically in the final minutes but despite the best efforts of the impressive Wayne Rooney, they could not force an equaliser.
Substitute Michael Owen had his shot cleared off the line by Nedum Onuoha and Rooney saw his rising drive turned over the top by an in-form Shay Given.
(reported from http://www.premierleague.com)
Tevez Dedicates Manchester United Victory To The Fans
“Obviously the talk was about Carlos [Tevez] before the game and he has done the talking on the pitch today with a great performance,” said Barry.
“That's the way it's written sometimes and the way Carlos works, he deserves it.”
The Manchester City midfielder believes there is still work to be done, however, if the Citizens are to progress to the final.
“It's still in the balance, half-time obviously, we know we can expect a tough game at Old Trafford. They're going to push on and give all they can and we've got to expect a battle again,” added the former Villan.
“We knew as individuals we were all going to have to dig deep and Shay's performed well.
“We're very delighted with the tie.”
Barry enjoyed the atmosphere in the stadium, and is hoping to draw out a similar reaction from City supporters in the second leg.
“It's obviously my first one here and the noise was tremendous at times. Hopefully we can give them something to shout about in the second game,” he concluded.
Tevez spoke briefly after the game, saying the fixture held a special significance for him.
“I feel ok, tired – but ok,” said Manchester City's match winner.
“[Beating Manchester United is] Very special for me and my team. It's for the fans of City.”