The two teams played out a goalless draw over 120 minutes of action with Chelsea producing a brave display against last season's winners, but City prevailed 4-3 on penalties with Jorginho and David Luiz missing for the Blues.
Chelsea went into the game without the use of a recognised centre forward, and it quickly became apparent that Eden Hazard would play in a deeper position in the middle.
That decision from Maurizio Sarri gave City the opportunity to control possession in the centre of the park, but for all of their dominance it took until the 22nd minute for a clear-cut chance to be created.
Chelsea improved as the first half progressed, but another opportunity went the way of Aguero who saw a deflected effort from the edge of the area comfortably saved by Arrizabalaga.
Hazard had remained a peripheral figure in attack, but Chelsea began to engineer spaces for their star man before the half-time whistle without the Belgian capitalising on time spent on the ball.
Nicolas Otamendi could have perhaps done better on the slide just before the break with a tame effort rolling through to Arrizabalaga, but the Argentine was fortunate not to put through his own net at the other end when attempting to deal with Willian's free kick.
A similar pattern of play continued after the restart with City seeing plenty of the ball, but their sole opportunity went to Fernandinho who volleyed high over the crossbar.
Aguero had the ball in the net just before the hour mark after a sharp turn and finish inside the area, but VAR confirmed the assistant's initial decision that the striker was offside by the narrowest of margins.
Chelsea advanced past the hour mark without conceding a goal, and the Blues soon created the best opportunity of the contest on the counter-attack.
Hazard was sent clear down the left flank and the playmaker had to remain patient before taking the ball past Vincent Kompany, but the Belgian's cutback was directed over the crossbar from 10 yards by N'Golo Kante.
The closing quarter of normal time became an end-to-end contest, and the introductions of Callum Hudson-Odoi and Sane for their respective sides suggested that both managers were keen to avoid extra time.
Chances remained few and far between with only Willian forcing a save out of either goalkeeper with a free kick, and Chelsea felt hard done by during the final minute of added-on time with Hazard being prevented from advancing through on goal by a contentious offside flag when play should have been allowed to continue until the end of the phase.
City began the stronger at the beginning of extra time but Chelsea were showing plenty of ambition going forward, and it left the City backline with questions to answer down either flank.
Jorginho curled a shot wide of the target after good play from Hazard and Hudson-Odoi, before Hazard fired harmlessly over the crossbar from a similar position on the edge of the box.
However, City began the second period of extra time by creating their best opportunity of the match through Sterling, whose cutback found Aguero only for Cesar Azpilicueta to stick out a leg and prevent the forward from tapping home into an empty net.
Aguero then forced a solid stop out of Arrizabalaga down to his left, and the Chelsea keeper appeared to suffer an injury in the process which led to Sarri calling for backup goalkeeper Willy Caballero.
However, Arrizabalaga refused to walk off the pitch and, after a stand-off between the pair, a seething Sarri eventually relented and allowed the Spaniard to see out the match.
The match went to penalties and both Arrizabalaga and Ederson made a save apiece from the first three spot kicks, but Luiz struck the post with Chelsea's fourth and it proved costly as Bernardo Silva and Sterling wrapped up victory for City and another trophy for Guardiola.
CHELSEA (4-3-3): Arrizabalaga; Azpilicueta, Rudiger, Luiz, Palmieri; Kante, Jorginho, Barkley (Loftus-Cheek 89'); Willian (Higuain 95'), Hazard, Pedro (Hudson-Odoi 79')
MANCHESTER CITY (4-3-3): Ederson, Walker, Otamendi, Laporte (Kompany 46'), Zinchenko; Fernandinho (Danilo 91'); D.Silva (Gundogan 79'), De Bruyne (Sane 86'); Bernardo, Sterling, Aguero
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