Sergio Aguero failed to equal Manchester City's goalscoring record but strikes from Kevin De Bruyne and Raheem Sterling secured a hard-fought win over Shakhtar Donetsk.
Aguero had a second-half penalty saved as he looked to pull level with Eric Brook's long-standing club record of 177 goals during City's Group F clash with the Ukrainian champions at the Etihad Stadium.
That was one of a number of frustrating moments for City during a tight contest, but a sublime strike from De Bruyne after 48 minutes and a late effort from Sterling secured a 2-0 victory.
The result took City clear at the top of the group with two wins from two games, three points ahead of both Shakhtar and Napoli, who visit Manchester next month.
Manager Pep Guardiola said: "We made an extraordinary performance, especially in the second half.
"We faced a team who demand a lot to beat them. It was a big victory for us. It is always complicated to play against them, that is why I am so satisfied."
Guardiola was not overly concerned about Aguero's frustrations, backing the Argentinian to reach Brook's milestone, which has stood since 1939, very soon.
He said: "That is going to happen. It doesn't matter today. He doesn't have to score 50 goals to break a record. It is just one."
De Bruyne and Leroy Sane missed good chances in the first half but Shakhtar also went close on a couple of occasions. Ederson produced a fine save to deny Marlos, and Fernandinho made a crucial tackle on Fred.
De Bruyne finally eased tension with a stunning long-range effort after the break and chances then became more frequent. Aguero spurned the best of them from the spot as Andriy Pyatov saved. The goalkeeper also kept out a fine Aguero volley.
Substitute Sterling, who earlier sliced wide in front of an open goal, wrapped up the win in the last minute.
After the game Guardiola also revealed left-back Benjamin Mendy, who suffered a knee injury in Saturday's win over Crystal Palace, could be facing a long lay-off. The club expect to learn the full extent of the problem later in the week after the Frenchman has visited specialist Dr Ramon Cugat in Barcelona.
Guardiola said: "Our first impression (is he) will be a little bit long, out of the picture, unfortunately for us."