Silva opened the scoring for a dominant Citizens side with a well-taken volley half an hour into the game, before Aymeric Laporte headed a deserved second into the back of the net.
City took their foot off the gas slightly in the second period, but they still added to their tally through Bernardo's edge-of-the-box strike 90 seconds after being brought off the bench.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Ederson; Stones, Laporte, Otamendi, Mendy; D.Silva, Fernandinho, De Bruyne; Sterling, Jesus, Mahrez
SUBS: Muric, Kompany, Aguero, Sane, Bernardo, Foden, Walker
STARTING XI: Pyatov; Matviienko, Kryvtsov, Rakitskiy, Ismaily; Maycon, Stepanenko; Wellington Nem, Kovalenko, Fernando; Moraes
SUBS: Shevchenko, Butko, Khocholava, Dentinho, Patrick, Bolbat, Kayode
Paulo Fonseca: "We will need to pay attention to all the players in the City team. They are very strong players and any of them can give us problems. We know it is going to be difficult and we will probably have to suffer a bit without the ball, but we will try to find ways to play our game and attack. Our principles remain the same, no matter who we play against. It doesn't matter who we are playing against - Manchester City or any other team."
Pep Guardiola: "In this competition you need something special, and still I don't feel it. I saw last season we are still not ready to win it. That's what I feel. That doesn't mean we are not going to try but to win this competition it's not enough just to have desire, or wanting to win. You have to have many circumstances, have experience and still we don't have enough in some moments. That's not enough that the manager wants to win it, it's not just the players. You have to have the desire - the club, chairman, owner, the fans, everyone has to push to be closer, to achieve the next stages. When it happens, everyone will feel it."
SHAKHTAR DONETSK SUBS: Shevchenko, Butko, Khocholava, Dentinho, Patrick, Bolbat, Kayode
MANCHESTER CITY SUBS: Muric, Kompany, Aguero, Sane, Bernardo, Foden, Walker