The meeting in west London was in stark contrast to the 1-1 draw played out in Manchester last week, with Jody Morris' side coming out on top in a repeat of last year's final and lifting the trophy in front of owner Roman Abramovich and first-team head coach Antonio Conte.
Chelsea started brightly and took the lead inside six minutes when Trevoh Chalobah looped a header into the top-left corner from Mason Mount's corner.
Dujon Sterling proved dangerous on the right flank and his delivery was turned home by an acrobatic, instinctive finish from Ike Ugbo midway through the first half.
Lukas Nmecha was kept out by Jamie Cumming before half-time, but he guided an exceptional finish past the Chelsea goalkeeper to reduce the deficit soon after the restart.
The Blues were unperturbed and Callum Hudson-Odoi restored their two-goal cushion by dribbling into the box and slamming an excellent finish into the top-left corner.
Sterling was next on the scoresheet for Chelsea, racing into the box after a one-two with Ugbo and beating goalkeeper Aro Muric at his near post.
Full-time: Chelsea 5-1 Man City (6-2 agg).— Chelsea FC (@ChelseaFC) April 26, 2017
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There was still time for more goals, substitute Cole Dasilva completing a 6-2 aggregate victory after Muric failed to hold George McEachran's strike.