City could easily have scored more goals but the win put the English champions top of the group on six points, a point clear of Lyon, who drew 3-3 at a Hoffenheim team who have two points along with bottom-placed Shakhtar
Manchester City began to show their credentials like proper Champions League heavyweights when they became the first English team to win at Shakhtar Donetsk in European competition with a handsome 3-0 success in their Group F match on Tuesday.
City, who false-started in the campaign with their only loss of the season at home to Olympique Lyonnais, were a wholly different proposition, waltzing to victory with goals from David Silva, Aymeric Laporte and substitute Bernardo Silva.
What looked a potentially difficult 1,700-mile visit to the Ukrainian champions, who had beaten Pep Guardiola's men in the group stages last year, was made to look effortlessly routine as the dazzling David Silva orchestrated their dominance.
City could easily have scored more goals but the win put the English champions top of the group on six points, a point clear of Lyon, who drew 3-3 at a Hoffenheim team who have two points along with bottom-placed Shakhtar.
City manager Pep Guardiola suggested on the eve of the match that the club may still lack the special passion for the competition that could drive them to European glory but his team of all talents demonstrated they certainly have the quality.
Shakhtar had never been beaten by English visitors in seven home matches, leaving Guardiola to appreciate the magnitude of the win. "Zero-three here," he said, "It's an amazing result.
"We've recovered with these two results in Germany (a win at Hoffenheim) and here. After the defeat against Lyon, it's in our hands again and winning our games at home will be the next stage."
The English Premier League leaders, with Kevin De Bruyne back for his first full start of the season after an injury layoff, continued their recent dazzling form by taking control from the opening whistle.
In the first half hour, Riyad Mahrez could and maybe should have scored twice, once after City had broken with breathtaking pace from their own half before he then also set up David Silva to flick the ball impudently against Shakhtar's post.
Yet the Spanish maestro made no mistake with a left foot volley just after the half-hour to reward City's mastery.
Five minutes later, De Bruyne's corner fell to Laporte, who found himself unmarked as he stooped to head home.
Though the home side attacked intermittently, City could have scored three more goals in the space of the first 12 minutes of the second half as they continued to pour forward.
Bernardo Silva had been on the pitch for 90 seconds after the excellent De Bruyne's withdrawal when another devastating City counter saw the Portuguese midfielder race through and slot his 71st minute left-foot shot in off the far post.
It sealed Shakhtar's first defeat in 12 matches in all competitions, leaving their chances of qualifying for the knockout stages looking bleak.
"We have to admit that City were better tonight. Much better," conceded Shakhtar manager Paulo Fonseca. "They won in good style. Our players tried to play well and keep the ball but it was not enough to stop a team like City."
It was a particularly enjoyable night for Shakhtar's former favourite Fernandinho, who was now at the heart of City's purring machine.
"I've enjoyed it," the Brazilian told BT Sport.