In Pep Guardiola’s first group game in charge, Aguero pounced to prod in an Aleksandar Kolarov cross and added a penalty kick when Ilkay Gundogan was fouled.
He rounded the keeper for his third in front of around 32,000 fans, a figure hit by Tuesday’s postponement.
Substitute Kelechi Iheanacho completed the scoring, firing in from 12 yards.
Monchengladbach, who saw nearly half their fans fly home before kick-off due to the rearrangement, offered little.
It just seemed a matter of time before Aguero added another treble to the one he hit against Steaua Bucharest in qualifying.
Monchengladbach goalkeeper Yann Sommer also produced two close-range saves to deny Aguero, as Guardiola’s side fired 23 attempts at goal against opposition which finished fourth in last season’s Bundesliga.
City’s Champions League record features two exits at the group stage, twice going out in the last-16 and a club-best semi-final place over five seasons.
Guardiola’s remit will be to take them further.
His record of reaching at least the semi-finals in his seven Champions League campaigns — including two triumphs with FC Barcelona — offers hope for the club’s following.
Against Monchengladbach, his side were far from the pass-heavy machine he built in Catalonia.
Instead they were efficient, seeing less of the ball than their visitors in the first-half but using it slickly to carve out chances and put the game to bed.
Substitute Kelechi Iheanacho completed the scoring, firing in from 12 yards.
(Edited and Controlled by Olawale Alabi)
