Leading 2-0 after the first leg, the Premier League leaders extended their overall advantage after only 12 minutes of the last-16 second-leg tie through Kevin de Bruyne’s excellent 20-yard left-footed strike.
Six minutes later, City scored again as Ilkay Gundogan slotted past goalkeeper Yann Sommer following a fine run and pass from Phil Foden, with the goal completing a 4-0 aggregate win.
Both matches in this tie were played at the Puskas Arena in Budapest because of coronavirus restrictions.
The draw for the quarter-finals is at 11:00 GMT on Friday.
City remain on course for a quadruple
This win means City have only lost one of their past 32 matches and keeps them on course to become the first English team to win the quadruple of Premier League, Champions League, FA Cup, and League Cup.
Before the match, defender Oleksandr Zinchenko said winning all four trophies was something City could achieve before boss Pep Guardiola later played down their chances.
This victory, and the manner of it, again shows that this City side, 14 points clear at the top of the Premier League, in the quarter-finals of the FA Cup and the final of the Carabao Cup, will take some stopping.
Guardiola started this ‘home’ match in Hungary without a recognised centre forward with Gabriel Jesus and Sergio Aguero among the substitutes.
However, Monchengladbach were unable to cope with the movement, speed of passing, creativity, and quality from City.
Foden had the first chance but flicked wide after Joao Cancelo’s ball over the top, but City soon went ahead with De Bruyne’s brilliant strike, which went in off the underside of the crossbar.
That was the 100th goal Guardiola’s team had scored in all competitions this season and the 101st quickly followed. Foden collected the ball in his own half, ran at the Gladbach defence, and produced a ‘no look’ pass to release Gundogan with the German scoring his 15th of the season.
De Bruyne had a further two chances to extend their lead but had a 30-yard free-kick pushed over and curled another shot wide from the edge of the penalty area, with Riyad Mahrez also having an effort saved.