The victory got the club back to winning ways after defeat to title rivals Liverpool and a draw with Sunderland but it was tarnished by the sight of Silva being carried off the pitch on the stretcher with an injury to his right ankle.
Coach Manuel Pellegrini said the injury, which will be assessed by medical staff on Tuesday, was a recurrence of an long-standing problem that caused the playmaker to miss last Wednesday's match against Sunderland.
"We will see tomorrow what happens with the doctor," the Chilean told the club's website.
"He couldn't recover in three days from his problem and that's why he didn't play against Sunderland. It's the same ankle."
City are six points behind leaders Liverpool and one behind Chelsea in the Premier League with a game in hand on both their rivals, who meet at Anfield on Sunday.
Silva, who has already missed two months of the season with thigh and calf injuries, has played an instrumental role in their challenge for a second title in three seasons.
Pellegrini might soon be able to welcome back his other most influential midfielder, Yaya Toure, after two weeks out with a groin strain, however, and said the plan for the rest of the season remained simple.
"I see the title race as the same this week as I did last week," he added.
"We knew we had two or three games postponed so it was difficult to be at the top of the table in that situation.
"We lost the game against Liverpool and we know we lost the chance to control our destiny but we have a duty to win the rest of our games and then see where that leaves us."
- Sports & Recreation
- Manuel Pellegrini