The Toffees took the lead in the 16th minute at the Etihad Stadium when Romelu Lukaku fired home, but Alvaro Negredo equalised moments later.
City then went 2-1 up when Sergio Aguero netted a neat finish, before the Argentine’s second-half penalty sealed victory for Manuel Pellegrini’s men following back-to-back defeats.
Silva was named man-of-the-match after a sparking display – and Milner admitted his delight at having the Spaniard available again after a thigh injury.
“It’s great to have David back, he’s a top player and any team in the world would miss him,” Milner told BT Sport.
“There’s great movement in the team, everybody’s comfortable on the ball and that’s what the manager’s encouraging, to play with freedom.”
Milner also praised City’s character for bouncing back from the Champions League humbling at the hands of Bayern Munich in midweek with a victory on Saturday.
“It was important we responded today,” he continued. “Obviously we had two disappointing results, two different performances.
“I think we played well at Aston Villa and probably didn’t deserve to lose the game. Then we didn’t perform to our standards in midweek so it was important we bounced back today against a very strong Everton team.
“I thought we did that, maybe we were a bit tired in the second half and didn’t finish the job as well as we could have done. But I think we showed great character after going a goal down.”
Silva, meanwhile, was delighted to be back in action. He added: “I’m very happy to come back to the pitch and happy for the team to win again. Now I want to keep going. We need to improve to go back to the top of the league.”
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