The Premier League leaders travelled to Ukraine fresh off the back of their 5-0 win vs Burnley.
Guardiola welcomed the return of Kevin De Bruyne following his return from a three month knee injury lay-off.
Man City stormed into a 2-0 half-time lead and simply blew the hosts apart.
Goals from David Silva and Aymeric Laporte put City in cruise control.
Moments after coming off the bench, Bernardo Silva fired a third in off the post.
The match finished 3-0 and City became the first ever English side to win away at Shakhtar Donetsk.
Pep Guardiola was particularly impressed with his side’s first-half performance.
“Our first half was the best first-half performance we have played in the last three seasons,” he told reporters.
“We created a lot of chances and didn’t concede any until the last few minutes.
“We were under a lot of pressure after the defeat by Lyon but now we are in a good position. We can control our destiny now.”
City moved to the top of Group F after Lyon were held at Hoffenheim.
The Ligue 1 side beat City at the Eithad on the opening match day.
The reigning Premier League champions now face a tough run of fixtures which sees them play three games in seven days.
They travel to Spurs next Monday before hosting Fulham in the Carabao Cup Round of 16.
Southampton are next to visit the Etihad in the Premier League on Sunday 4th September.