The Citizens initially failed to break the defense of a resilient Aston Villa side despite producing 13 shots in the first half.
The Villans came out after the break with similar set up and the game seemed to be heading for a stalemate before Silva broke the deadlock with a controversial goal on the 79th minute mark.
In-form Ilkay Gundogan then rubbed salt in Aston Villa’s injury in the final minute after Matty Cash was ruled to have handballed in his own penalty area, leaving the German to beat Emiliano Martinez from 12 yards.
"It was a very important win, a tough game for us. just three more points and on to the next one,” Silva said after the game.
"It felt like an important win because we got to 75th minute without scoring, so to get those two goals, we're very happy.
"Its been a long time since I have scored. I'm happy to score. It doesn't matter who scores the goals but I'm happy to score. There is still a long way to go but still, very happy.
"We're doing very well, very solid at the back. We are happy with the last two games and our momentum."
Next up for Silva and Manchester City is a game in the FA Cup against Cheltenham on Saturday before a trip to face West Bromwich on January 26.
