The 25-year-old Argentinian, who is currently waiting for a decision as to whether his two-year loan spell will end in a permanent move to United, was outstanding in a game which was well below par to the usual blood and thunder occasion.
The Red Devils were always in control as they avenged City's league double of last season with one of their own this time around.
It was Tevez who was the first United player to test Shay Given when his 25-yard drive in the fourth minute was taken at full stretch by the Citizens goalkeeper.
United took the lead after 18 minutes.
Stephen Ireland wrapped his legs around Dimitar Berbatov's legs 30 yards from goal and Cristiano Ronaldo stepped up to blast the resulting free-kick right-footed into the bottom right corner of the net, courtesy of deflections off Nigel de Jong and Given's left hand.
Tevez was unlucky not to get on the scoresheet in the 31st minute. Picking up a pass inside from Patrice Evra after his run down the left, Tevez hit a tremendous right-foot shot from the left corner of the penalty area which crashed against the City bar.
But United's first-half dominance was properly reflected when they doubled their lead in the closing seconds.
Darren Fletcher's long ball out of defence was brilliantly taken down in one movement by Berbatov 25 yards from goal.
The Bulgarian striker turned superbly and played the ball to his right for Tevez to hit a viciously curling right-foot 20-yard shot in off the right post.
The second half was an anti-climax as the game became strewn with misplaced passes and untidy play.
It could have been different had City striker Robinho not fired high and wide when well placed eight yards out in the 51st minute.
Ronaldo showed his obvious dislike being replaced by Paul Scholes in the 59th minute as he walked off.
City substitute Martin Petrov forced United goalkeeper Edwin van der Sar to make his only real save of the game four minutes from time, when the Dutchman hurled himself across goal to tip behind the Bulgarian winger's fierce 30-yard shot.
But United were unlucky not to make it 3-0 in the final seconds when Darren Fletcher's header from a Wayne Rooney corner hit a City upright after the magnificent Tevez had got a faintest touch to the ball inches from the far post.