The visitors took the lead shortly after the interval through Jude Bellingham, but John Stones struck a thunderous equaliser with ten minutes left to play.
Four minutes later, Haaland bagged his 13th goal of the season in all competitions with an acrobatic volley from Joao Cancelo's superb outside foot cross.
The Norwegian striker admitted that he was proud of the response from City after falling behind.
"In the end we showed what we are, this is what we are and this is how we have to play.
"I’m proud of the last 20 to 25 minutes. We scored two wonderful goals today, mine was a bit better honestly! Nice cross from Cancelo."
The win sees Pep Guardiola's men remain top of Group G in the Champions League after two fixtures.
22-year-old Haaland, who joined City from Borussia Dortmund in the summer, also took the time after the game to direct some praise to his former club, who frustrated City for large periods of the encounter under the floodlights.
"It’s good to see everyone from Dortmund. They didn’t stop me, I scored!
"They played well, they were good. I was quite sure I was going to be followed the whole game because Edin [Dortmund boss Terzic] knows me very well.
"Dortmund was really good today. In the end, the three points is what matters."