Kelechi Iheanacho also got on the scoresheet late on as City made up for lost time after torrential rain washed out the first attempt to play the fixture at the Etihad Stadium on Tuesday.
Aguero, currently suspended from league action, opened the scoring after nine minutes, added a second from the penalty spot and completed his treble after 77 minutes before Iheanacho added a fourth.
It was another highly convincing performance by City, who did not even seem to get into top gear as they cruised to a seventh successive win under Pep Guardiola.
City, much like last weekend’s derby against Manchester United, were superb in the first-half, with their movement quick and passing crisp and this time maintained their domination for longer.
Ilkay Gundogan, making his debut after David Silva dropped out of the side named for the original game as a precaution, immediately looked the part. The German, playing his first game since suffering a knee injury in April, drove City forward and linked well with Kevin De Bruyne and Raheem Sterling.
City wasted no time in taking the lead, with Aleksandar Kolarov driving a good low ball into the box and Aguero pouncing in typically clinical fashion from close range.
Further damage seemed likely as Fernandinho released De Bruyne with an incisive through ball and Aguero teed-up Gundogan but goalkeeper Yann Sommer beat away his shot. Gundogan then turned provider for Sterling but Sommer took the sting out of the England winger’s drive and Tobias Strobl cleared.
Aguero gave City a scare when he seemed to suffer a knee injury after a collision with Nico Elvedi but he opted to continue after treatment.
His decision was soon vindicated with a second goal as he struck from the spot after Gundogan was tripped on the edge of the area by Christoph Kramer.
Borussia were being completely outplayed and coach Andre Schubert took Kramer off after 38 minutes.
The visitors then enjoyed their best spell with Lars Strindl bringing a good save out of Claudio Bravo just before the interval.
City went back on the offensive after the break and confusion in the Borussia box handed Aguero a chance but Sommer palmed over the crossbar. De Bruyne also tested the keeper with a low drive.
Sterling seemed certain to make it 3-0 after being sent clear by De Bruyne but delayed his shot and Sommer blocked. But Aguero was not to be denied his hat-trick and showed great composure to guide the ball around Sommer and tap home.
He was replaced seven minutes from time to a huge ovation and his replacement Iheanacho rifled in a fourth in time added on.
Bravo, Zabaleta, Otamendi, Stones, Kolarov, Fernandinho, Jesus Navas, De Bruyne, Gundogan (Clichy 81), Sterling (Sane 79), Aguero (Iheanacho 83).
Sommer, Elvedi, Christensen, Strobl, Johnson, Dahoud, Kramer (Korb 38), Wendt, Stindl (Traore 81), Raffael, Hahn (Hazard 59). Subs Not Used: Sippel, Vestergaard, Hofmann, Jantschke.
Bjorn Kuipers (Holland).