The Blues dominated from start to finish with first-half goals from Riyad Mahrez and Ilkay Gundogan and a late third from Gabriel Jesus the perfect response to the weekend defeat at Norwich.
Almost from the word go, City pinned Shakhtar back in their own half, dominating possession and restricting the hosts to the occasional foray forward.
A number of half chances were created without testing the home goalkeeper, but as the half progressed, so City looked more and more likely to break the deadlock.
The breakthrough finally came on 24 minutes when Ilkay Gundogan’s curling effort from the edge the box smacked the post and fell invitingly to Riyad Mahrez who thumped the ball into the unguarded net.
It was no more than the Blues deserved for their near total control.
For Shakhtar, so used to bossing games in the Ukraine Premier League, it must have felt like a chiding experience in front of their own fans.
Indeed, Ederson wasn’t called into action until the 35th minute when a clever through ball from Barcelios Freda put Ribeiro Moraes Junior in sight of goal but the City keeper made himself big and beat the shot away.
Three minutes later, City doubled the lead with Mahrez spotting Gundogan’s burst into the box and the German finishing emphatically from eight yards.
Just before the break, Kevin De Bruyne raced on to Gabriel Jesus’ pass and shot just wide of the post – it had been an impressive half by the Premier League champions with the home side becoming increasingly overrun.
Shortly after the re-start, Moraes reminded the Blues there was still work to do as he raced clear and with Ederson on the edge of the box, should have done better with his shot towards and empty net.
But Sterling would no doubt have felt the same moments later as he was gifted a shot at goal following Gundogan’s fierce shot, only to see his shot from close range hit the outside of the post and out of play.
So many half chances were created and missed, it was a mystery how City weren’t out of sight by the midway point in the second half with the danger being a goal for the hosts would make for an uncomfortable last 20 minutes or so.
But those fears were dispelled 15 minutes from time when a City counter-attack saw three-on-one and De Bruyne's pass put Jesus clear and the Brazilian finished with a smart low shot just inside the post.
That was effectively the end of the contest and completed a fine away win for a much more familiar looking City.
City’s immediate response
City needed to get the defeat at Norwich out of their system quickly – and the response couldn’t have been more emphatic.
Nicolas Otamendi returned to the right side of the central defensive partnership and Fernandinho effortlessly slipped in alongside him with a calm, cool performance that oozed class.
It will cheer Pep Guardiola, who has two injured central defenders on the sidelines already this campaign - as will the late cameo from Benjamin Mendy, who made his long-awaited return near the end of a very comfortable evening for the Blues.
Star man: Ilkay Gundogan
A goal, an assist and he could have had more, the German midfielder was impressive throughout.
What it means…
Dinamo Zagreb's 4-0 win over Atalanta means City are second in Group C after Matchday 1.
"I'm thinking already about Watford as we don't have much time, but to start away in the Champions League and get a good result is fantastic.
"The way we played was very good, we created incredible chances, but all the guys were fantastic. Better than last season!"
City return to Premier League action this Saturday with Watford visiting the Etihad Stadium (3pm kick-off).