Moussa Dembele scored early in both halves for the hosts in Glasgow either side of a Raheem Sterling own goal
Manager Pep Guardiola tempered his delight at Manchester City's ability to fight back three times in a thrilling 3-3 draw against Celtic in the Champions League on Wednesday by urging his players to understand the importance of a good start.
Moussa Dembele scored early in both halves for the hosts in Glasgow either side of a Raheem Sterling own goal as City responded each time with strikes from Fernandinho, Sterling and Nolito.
The Premier League leaders are second in the group on four points, two behind Barcelona, who rallied to win 2-1 at Borussia Moenchengladbach in the other Group C fixture.
"Maybe this is a good lesson for our future on the importance of starting well," Guardiola told reporters.
"It was difficult for us to start in the first half and second half with a goal against us, that's why I'm so happy for the reaction of the players -- it's not easy to score three goals away.
"This group, this club, we are going to fight until the last game to qualify."
City defender Pablo Zabaleta praised the team's character in finding a way back to fight back at Celtic Park on three different occasions.
"To come back three times when we were behind shows the character of the team. We were a bit unlucky not to score at the end. We created a few clear chances and had control of the game in the second half, Zabaleta said.
"It's true that we conceded in three key moments of the game, especially the third goal at the start of the second half but to come back was important."
City, who top the Premier League standings after winning their opening six games, travel to Tottenham Hotspur in a contest between two unbeaten sides on Sunday.