Two near-identical goals, one scored by Bernardo Silva and the other assisted by him, put Pep Guardiola’s side within touching distance of the quarterfinals.
Bernardo put City in front on 29 minutes, losing his marker at the back post to head home a pinpoint Joao Cancelo cross.
The same move resulted in Bernardo heading back across goal for Gabriel Jesus to tap in on 65 minutes and put City in a commanding position with two away goals.
The tie took place at the Puskas Arena in Budapest, Hungary, rather than in Monchengladbach, due to German authorities putting travel restrictions on the UK amid the spread of a COVID-19 variant.
City are 10 points clear of second place in the Premier League, in the Carabao Cup final and in the quarterfinals of the FA Cup as they chase an unprecedented quadruple.