Jonathan is ESPN FC's Manchester City correspondent.
Guendogan nearly equalised soon afterwards but his low shot saved by Yann Sommer.
Gladbach then had captain Lars Stindl sent off on 50 minutes for a second yellow card and then Fernandinho followed him for City with his second yellow after pulling back Raffael.
City are third in the Premier League with 27 points, 13 ahead of 12th-placed Burnley after 12 games. Following the match, Pep Guardiola told BBC Sport he was happy to be in the Round of 16.
Yet when asked about the importance of defeating Burnley before embarking upon all of this, Guardiola said: "It will be complicated for the other teams as well. It was a tough game but the most important thing was the result". He played there in Barcelona once, the Champions League final against Manchester United, because we have a lot of problems there.
Want your voice heard? "(City) are a fantastic team. The Bundesliga outfit have continuously failed to capitalise on good starts as a result of undisciplined and inconsistent performances.
Cenk Tosun's fantastic volleyed goal sparked a wild comeback as Besiktas fought from three goals down to salvage a 3-3 draw against Benfica in Group B.
The Clarets have the 4th best home form in the league so far. Granted they did advance to the knockout round Pep still has some work to do with the attacking side of the team.
The hosts were risky on the counter-attack and served warning of their threat as Fabian Johnson had a shot blocked and then forced a save from Claudio Bravo after being played in by Raffael.
Guardiola is bracing himself for a tough test against Sean Dyche's team, who have proved hard opponents for top teams.
City's John Stones, who had earlier been nutmegged by Nico Elvedi, lost out in the air to Stindl, who charged to the edge of the box.
With Kompany's loss, Guardiola faces selection headaches as he has to find the right fit at centre-back along to partner Nicolas Otamendi. Kevin De Bruyne and David Silva were superb in the midfield creating chances and working the offense through themselves.
The game was paused for a moment when a bottle thrown from the crowd landed close to Sergio Aguero but it was an isolated incident.
"Obviously they can be fully focused on the Premier League".
City visits Burnley in the league on Saturday.
City's performance was a little underwhelming after the highs of beating Barcelona but it was a professional one and De Bruyne and David Silva were the key men.
The positive is Manchester City are through to the next round, with a game to spare.