Second-half substitute Georgios Samaras sparked a City revival with two goals as Stuart Pearce's men claimed their first home victory since November.
Samaras ended a 17-game goal-drought at Eastlands
City burst into life after a dismal first half when Samaras slotted home DaMarcus Beasley's cross 49 minutes in.
He then fired in a penalty 21 minutes later after keeper Tim Howard brought down Darius Vassell.
Everton's Leon Osman clawed a goal back late on but could not stop City sealing their third straight league win.
Although City officials have rejected reports of a £13m bid for Micah Richards, his undeniable talent looked wasted in a tough opening 45 minutes for the home side.
City headed into the game looking confident after 1-0 wins over West Ham and Sheffield United but struggled to conjure up decent chances early on as opponents Everton dominated possession.
David Moyes' men, fresh from their emphatic 3-0 win against Newcastle two days ago, really should have made more of their opportunities.
Joseph Yobo's weak header was easily dealt with by City keeper Nicky Weaver and the visitors were unlucky to have a penalty claim turned down in the 15th minute when Richard Dunne appeared to shove Andrew Johnson over in the box.
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Richards, pushed into central midfield, hit wide with a speculative long-range effort on the half-hour mark and, in the 41st minute, Bernado Corradi and Darius Vassell failed to scramble a City free-kick goalbound.
But a different City side emerged from the tunnel in the second half with manager Stuart Pearce instantly reaping the rewards of replacing ineffectual striker Corradi with Samaras.
Just four minutes after the break, the muted home fans roared into life as Greek striker Samaras latched onto Beasley's probing cross from the left to slot home from six yards.
Everton looked on the backfoot after that, with Samaras continuing to look dangerous going forward.
He doubled his tally in the 70th minute after Howard's rash challenge on Vassell resulted in a penalty, driving the ball into the top right-hand corner of the net.
It marked the end of a 17-game goalscoring drought for Samaras, who helped City welcome the New Year on a winning note.
Everton desperately looked to get back into the game and saw a glimmer of hope when Osman pulled a goal back with seven minutes to go, firing in Phil Neville's cut-back from the right.
But more frustration followed for the Toffees as referee Uriah Rennie refused to award a penalty when Sylvain Distin appeared to bring down Osman in stoppage time
In the end, City held on for all three points and sealed their first win at Eastlands since victory against Fulham in November.
Manchester City boss Stuart Pearce:
"Georgios is a 21-year-old playing in the Premiership for the first time in
"He's a young man learning the game in the hardest league to learn.
"He has a fantastic aptitude to want to learn and he turned the game against Everton. Anyone who can do that in the Premier League has to be respected."
Everton boss David Moyes:
"Our first-half performance merited more but our second-half performance didn't merit anything.
"We didn't create enough chances when we had the good play.
"But we should never put ourselves in the position where we lose a goal four minutes into the second half and then we gave away a bad second goal."
Man City: Weaver, Onuoha, Dunne, Distin, Trabelsi (Miller 85), Richards, Dabo, Beasley, Jordan, Corradi (Samaras 46), Vassell.
Subs Not Used: Isaksson, Dickov, Matthew Mills.
Booked: Trabelsi, Miller.
Goals: Samaras 50, 72 pen.
Everton: Howard, Neville, Yobo, Lescott, Nuno Valente (Naysmith 46), Davies (McFadden 65), Carsley, Arteta, Osman, Johnson, Beattie (Anichebe 65).
Subs Not Used: Wright, Weir.
Booked: Howard, Arteta, Johnson.
Goals: Osman 84.
Ref: U Rennie (S Yorkshire).