Mancini's changes prove to be golden as the Italian striker and England midfielder came off the bench to seal a tough win following a solid defensive display from the Toffees
It was the Toffees who started the better of the two teams, asserting early pressure on City's creative players and carving a few half-chances for themselves.
City had the first good chance to score however, when Phil Jagielka's attempted header to goalkeeper Tim Howard was too short and Edin Dzeko looked to capitalise, intercepting and rounding the American, but Jagielka recovered well to steal the ball from the Bosnian striker's toe.
Despite being shadowed by Jack Rodwell over the entire pitch, David Silva shook off the youngster, playing the ball through Rodwell's legs and crossing for Dzeko, but Jagielka was on hand again to clear.
Rodwell became the first player to go into referee Howard Webb's notebook after going through the back of Silva and this was the first of a flurry of bookings with, Leon Osman, Phil Nevilla and Yaya Toure all being shown the yellow card in a short space of time.
City struggled to break down the Toffees' backline but looked dangerous as Micah Richards overlapped down the right, but his cross was just behind Dzeko who couldn't direct his shot on target.
Aguero then showed his class with a curling effort from just inside the box which Howard did well to turn away from a corner, the American also dealing with Gareth Barry's volley comfortably.
Dzeko and Toure both had speculative long-range efforts that failed to hit the target before the half-time whistle saw the teams go in for the break without a goal between them, with Everton likely to have been the more satisfied.
The second half saw City issue an early statement of intent, with Aguero looking especially lively, having a couple of early efforts at Howard's goal.
Leon Osman also saw his effort fly straight into Joe hart's gloves as Everton looked to create opportunities of their own, whilst Tim Cahill also saw a looping header go over the crossbar.
City were still unable to worry Everton despite a majority possession and they made a change on the hour as Balotelli replaced Dzeko, who failed to live up to the Player Of The Month award he received before kick-off.
The substitution proved to be inspired as Aguero cut infield and played the ball into Balotelli who hit a shot from 20 yards that deflected off Jagielka and beat Howard to give City the lead.
The goal energised City who could have scored a quick second as Silva tricked his way into the area, his first effort was blocked but the ball fell back to the Spaniard who rattled the post with his follow up, before Balotelli also fired just wide from the resulting corner.
Everton, who had already brought on Louis Saha for the injured Cahill, introduced Royston Drenthe and Apostolos Vellios in an attempt to rescue the game, City making defensive minded changes as Milner and Stefan Savic replaced Aguero and Nasri.
It was still City who were looking more dangerous, however as Toure hit another long-range effort that Howard did well to keep out low to his left, Silva also netted from an offside position following Balotelli's low cross.
City finally grabbed a second as Silva beat his marker and played an inch-perfect through ball to Milner who turned in his first Premier League goal since his big-money move to Eastlands last season to wrap up the three points for the home side.