Many expected Group F to be a formality for City, but Pep Guardiola's Premier League champions lost their opening game at home to Lyon to blow open the group.
City then went a goal down to Hoffenheim in the first few seconds of their next game, but recovered to earn a vital 2-1 win in Germany.
Guardiola's men now face a trip to Ukraine to face Shakhtar, but will have to be on their toes after losing there 2-1 in last season's group stages.
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TV, online and live stream coverage
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Betting tips via Betfair | UK users only | Subject to change
- Man City to win 2-0: 15/2
- Shakhtar to win 2-1: 14/1
- 1-1 draw: 9/1
Click here to find the latest match odds and place a bet.
Head to head
The two sides have met twice before, in last season's competition. City won 2-0 at home, but lost 2-1 away.