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.
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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.
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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.
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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.
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