On-loan Liverpool striker Fabio Borini gave Sunderland an early lead at Wembley but superb goals in quick succession from Yaya Toure and Samir Nasri turned the game and Jesus Navas added a late third.
The match came less than a year after City were shocked by Wigan in the FA Cup final and Sunderland deservedly led at half-time.
But City were a different side after the break and Toure's sweeping first-time shot in the 55th minute drew them level.
The second arrived less than two minutes later, Nasri lashing in Sergio Aguero's deflected cross, and Navas finished the job in the 90th minute to give City their first title in the competition since 1976.
It brought Manuel Pellegrini a first trophy in English football, and the Chilean immediately set his sights on further silverware, saying: "We wanted this trophy but I don't think that anybody can think that is enough. I don't think for top players or important clubs, you are satisfied with one trophy.
"Maybe what happened last year in the final was on their minds in the first half but I think that the most important thing was to calm the players and trust in them.
"I told the players they had 45 minutes to change the score. It was important for the players to be calm and they were."
City went on to win their second Premier League title in three years but lost to Wigan again in the quarter-finals of the FA Cup and Barcelona in the last 16 of the Champions League.