A fine finish and a first-half penalty secured an early brace, before he slotted home with his usual calmness to bring up his third goal.
Kelechi Iheanacho grabbed yet another goal, in what was a night to forget for the Foals.
From the teams that were set to start last night David Silva was left out after not feeling just right, according to Pep Guardiola. That left room for Ilkay Gündogan to make his Manchester City debut. For André Schubert, the same side meant to begin the game on Tuesday took to the field.
City take control of the game from the off
The opening few exchanges were tense, as both looked to the wings for early inspiration. The majority of chances were snuffed out by slide tackles, but eventually City's perseverance paid off. A superb low ball into the near post from Aleksandar Kolarov found Aguero's darting run; he was able to flick into the top corner with nonchalant ease.
It could have been two moments later as City shifted the ball superbly across the box, as it eventually ended up with Gündogan. His shot was well-saved by a sprawling Yann Sommer, though. The Swiss goalkeeper soon had Andreas Christensen to thank for vital interceptions as Raheem Sterling almost found Aguero on two occasions.
The Argentine didn't have to wait much longer for his second, and was handed the perfect opportunity to grab his brace when Christoph Kramer fouled Gündogan just inside the area. Aguero sauntered up to the spot with his usual swagger and sent Sommer the wrong way to put City in pull control of the game.
Gladbach's only real form of resistance came from Lars Stindl, who had a shot well-blocked by John Stones before bringing a superb save out of Claudio Bravo. The 'keeper could have been forgiven if he had switched off just before the break, but instead reacted quickly to palm away Stindl's effort and maintain City's two-goal lead.
More of the same in the second half
The hosts picked up where they left off before the interval and almost found a quick-fire third. After Sommer spilled a relatively tame initial effort, City recycled the ball and fed Aguero, only for the Swiss to redeem himself with a good save high to his left. From then on, the tempo in the game began to die a slow death.
It wasn't until late on that Guardiola's men picked things up again and caused Gladbach further problems. Kevin de Bruyne sent Sterling through on goal, only for Sommer's legs to narrowly divert his effort past the post and wide. The visiting goalkeeper then denied Aguero with his feet in the follow up attack.
The forward would not be denied his hat-trick, however, as Sterling fed Aguero and he left Sommer on the ground before passing into an empty net. To add insult to injury, Iheanacho finished off a fine move between de Bruyne and Leroy Sané for City's fourth. They certainly mean business in this year's competition.