After multiple missed chances for both sides, Bernardo Silva opened the scoring in sublime style as he finished off Joao Cancelo's cross to the back post with a deft header.
The second half saw Silva become goalscorer-turned-provider as his stooped header across the box was poked home by Gabriel Jesus to make it two.
City pushed through the rest of the first leg to take a respectable 2-0 lead back to Manchester. Borussia Mönchengladbach will be disappointed with themselves for giving two away goals to the Premier League leaders, and definitely disappointed not to score.
Wednesday night's outing in Hungary made it 100 appearances in City blue for Aymeric Laporte, as the Frenchman paired up with Ruben Dias to fight off their German opponents.
Although not having to deal with the most dangerous of attacks, Laporte was always switched on and smothered any counter-attack Mönchengladbach were forming.
City's £57million-man has seen far fewer minutes on the pitch this season, being kept on the bench by the in-form duo of John Stones and Dias. It is clear, however, that Laporte's form is permanent as when he does play, it is as if he never left the Starting XI.
For any Citizens watching on the night, most will have been watching from behind the sofa as Raheem Sterling missed multiple opportunities, which could have ultimately ended the tie after 20 minutes.
However, it is Mönchengladbach that will regret the chances they failed to take. Alassane Pléa and Marcus Thuram both managed to get in behind the City defence, but all through balls were just long enough for Ederson to come out and sweep up - the only action the Brazilian really had.
City then created two beautiful chances that inevitably punished the German side, leaving Marco Rose's rueing the missed chances.
Florian Neuhaus failed to capitalise on a mistake from Rodri as his backpass was pounced on by the German. His shot was the final kick of the game, an important kick that could have kept Mönchengladbach in the tie, halving the deficit. However, it was an easy catch for Ederson and so, the German side came away from the game with nothing.
Another record broken
A 2-0 win on Wednesday night in Hungary meant City have set a new top-flight English record for consecutive away victories, moving ahead of the previous record with 12 away wins (also set by Pep Guardiola's men between May and November 2017).
Those 12 wins coincide with their ongoing record-breaking stat - 19 consecutive wins in all competitions. City are unbeaten in 26 games, with the last defeat coming against Tottenham Hotspur all the way back in November.
City supporters will hope to see their unbeaten run carry on in the tournament as they aim to win the club's first Champions League trophy.
Agüero back in action
Sergio Agüero's cameo on Wednesday in the Champions League saw the Argentine play his first few minutes in the last 11 games.
The club legend got straight back into the action with a smart swivel on the spot before feeding Riyad Mahrez in on goal, but the winger was unable to get the assist Agüero would have been craving after so long on the sideline.
His season has been plagued by injury and Coronavirus, meaning the striker has only played a total of 270 minutes all season.
The performance against the German side will hopefully spark the rest of his season and the forward will be able to add to his tally of two goals before the season ends. The recovery could be perfectly timed with City struggling in some games at the top end of the field.