Robin van Persie broke the deadlock in the 16th minute, deftly guiding a shot into the top-left corner after an enterprising run down the left flank from winger Ashley Young.
Tom Cleverley's fine finish, following a one-two with Michael Carrick, made it 2-0 three minutes later, before van Persie teed up strike partner Wayne Rooney for United's third just before the hour.
United captain Nemanja Vidic made his return following a long-term knee injury as a second-half substitute and even a 72nd-minute header by Sunderland's former United striker Fraizer Campbell could not spoil the hosts' day.
Defending champions City had returned to winning ways earlier on Saturday with a 3-1 victory at Newcastle.
Beaten 3-2 by their cross-town rivals in a fiery Manchester derby last weekend, the champions showed no ill-effects in the early stages at St James' Park and took the lead in the 10th minute with a beautifully crafted goal.
Stand-in captain Yaya Toure split the home defence with a delicately weighted pass down the inside-right channel and Samir Nasri showed excellent awareness to roll the ball square for Sergio Aguero to tap into an empty net.