Silva fell to the ground after a tangle involving Morgan Amalfitano and Billy Jones in the 67th minute, and after treatment was given he departed down the tunnel with his right leg in a brace.
Two goals in the first 10 minutes had paved the way for City to keep the pressure on leaders Liverpool and avoid any repeat of their surprise home draw with bottom-of-the-table Sunderland last week.
Pablo Zabaleta got the home side off to a flying start and Sergio Aguero quickly added a second. Despite a superb strike from Graham Dorrans which briefly reduced the deficit, a close-range effort from Martin Demichelis effectively wrapped up a win which leaves City six points behind the leaders with one remaining game in hand.
The visitors, who stay hovering just three points above the drop zone after this latest setback, showed plenty of promise on the break but were let down by some dismal defending, and were ultimately fortunate not to find themselves on the end of a heavier defeat.
There was certainly a degree of fortune about City's third-minute opener as Ben Foster saved superbly from Aguero but could only flap the ball straight at Zabaleta, who headed back into the net.
Aguero then blazed over the bar before West Brom offered a reminder of their sporadic counter-attacking threat when a swift move ended in Matej Vydra bundling the ball into the net only to be ruled offside.
Edin Dzeko was denied by a crucial Jonas Olsson block in the box before Aguero found space 20 yards out to drill a low effort across Foster and into the corner of the net to double City's lead. The home side looked like taking full advantage of an opportunity to boost their goal difference, but the visitors proved adept at exploiting the open spaces afforded them and after Stephane Sessegnon shot just over the bar, Dorrans got his side on the board with a superb strike.
The Scot was played in by Vydra down the right flank and, after two expert flicks on the edge of the box, he drilled a fine effort home to Joe Hart's left. Suddenly some nerves became evident in the City back-line with Hart spilling a Chris Brunt free kick before referee Phil Dowd flagged for offside, but City's third goal brought an end to the revival.
Samir Nasri sent in a corner from the City left and the ball evaded everyone in the box before falling at the feet of Demichelis, who could hardly believe his luck as he bundled home from six yards.
In a much more low-key second half Foster got in bravely at the feet of Dzeko to deny City a fourth, before the departure of Silva - moments after an uncomfortable-looking Aguero had been replaced by Stevan Jovetic - caused consternation in the City ranks.
Another West Brom substitute, Saido Berahino, had a penalty shout rejected by Dowd before Dzeko curled his late effort inches wide after a neat lay-off from Jovetic.
James Milner, a substitute for the hosts, had the last chance of the match when he drilled a low injury-time effort which was well saved by the impressive Foster.