The Chilean was brought to the club with the remit of winning silverware and, though City was behind at the break, he duly delivered at Wembley on Sunday thanks to wonder goals from Yaya Toure and Samir Nasri, with Jesus Navas adding the third late on.
Gus Poyet's men played their part in an exhilarating contest and Fabio Borini's superb opener left City fans fearing more Wembley disappointment following the 1-0 defeat to Wigan Athletic in May's FA Cup final.
But, ultimately, City lived up to the favorite tag to leave the club's hopes of a quadruple still on course, though the team will have to overcome a 2-0 deficit against Barcelona in their Champions League tie.
Despite controlling the early tempo, City was given a warning when Jack Colback tapped home Borini's slide pass, but the whistle had long since gone for offside.
Having survived that scare, Sergio Aguero, making his return from a month-long injury absence, made his first contribution on nine minutes when he forced Mannone into a smart save from 20 yards.
Just a minute later the Sunderland fans were sent into raptures. Johnson floated a superb ball from the halfway line that Borini collected on the edge of the area before holding off the challenge of Kompany and applying an expert finish with the outside of his boot.
There was no let up from Sunderland, which caused havoc with two corners as first Borini saw an effort from the edge of the box deflected over, while Wes Brown put a free header wide.
A clearly rattled City gradually began to exert some pressure and Borini had to be on hand to clear the danger inside the six-yard box after Aleksandar Kolarov's flicked header.
Poyet's men still looked remarkably assured, however, and it required a superb last-ditch tackle from Kompany to prevent Borini having another opportunity to score on 38 minutes after the Italian had broken free of the defense.
Seeking a swift response after the break, City saw David Silva hit a tame effort at Mannone, before at the other end Ki Sung-Yueng's flash shot from distance forced Costel Pantilimon into action.
The game then turned on two unstoppable strikes in as many minutes.
First Pablo Zabaleta, sent off in the Wigan reverse, played the ball square to Toure, and the Ivorian planted his long-range strike into the top corner from 30 yards.
City stole ahead on 57 minutes. Kolarov's cross from the left was deflected into the path of Nasri, who connected with a sweetly struck first-time shot that flew into the corner of the goal.
Sunderland refused to lie down but it was City which looked more likely to score again, with Kompany's near-post volley flashing just wide in the closing stages.
The result was sealed in the last minute when Navas put the finishing touch on a swift breakaway.
Poyet will now turn his attention to Sunderland's fight for top-flight survival, while Pellegrini's side has matters to attend to at the other end of the table, with a six-point gap to league leader Chelsea having opened up over the weekend.