Gabriel Jesus scored either side of Willy Boly's 19th-minute red card to put the Citizens in complete control by the break, but the only further damage to Wanderers was Conor Coady's own goal as the visitors battled to the end.
An 11th win from 12 home matches in the top flight this season not only reduces the gap to Liverpool but takes City five points clear of Tottenham Hotspur in third.
The Citizens had scored 16 goals in their last two outings and looked in the mood prior to Boly's dismissal, taking the lead inside 10 minutes via a classic Pep Guardiola move.
Making his club-record 267th Premier League appearance for City, David Silva nearly marked his landmark outing with a goal when his deflected strike from the edge of the box threatened to loop underneath the crossbar before Rui Patricio pushed it over.
Wolves claimed the scalps of Spurs and Liverpool over the festive period but their hopes of another giant-killing were effectively over after 20 minutes as Boly lunged into a challenge with Bernardo Silva studs first and caught the Portuguese on the ankle.
That being said, the visitors did have one golden opportunity to equalise on 36 minutes, only for Jonny to waste a really promising three-on-three break by attempting to square to Diogo Jota, rather than take on the shot himself after being released into the box.
Two minutes later, Ryan Bennett conceded a penalty for a clumsy trip on Raheem Sterling, and Jesus stepped up to slot his seventh goal in three matches into the bottom corner, justifying his selection over Sergio Aguero who was afforded a rest on the bench.
City could have been three up before half time but Sterling headed Danilo's cross straight at Patricio from the centre of the box.
Guardiola's boys were ruthless going forward against lower-league Rotherham United and Burton Albion in two cup ties last week, but seemed to make a concious decision to cruise through the second period ahead of a run of five fixtures in the space of 15 days.
Patricio still had to be alert to save from long-distance Kyle Walker and Fernandinho efforts, while Sane squandered a good chance at the back post when he scuffed horribly wide on his weaker right foot, following skilful link-up play between Sterling and Bernardo.
The ante was upped a little when Kevin De Bruyne continued his recovery from injury with a half-hour cameo, and the Belgian did not take long to affect the game, rifling a shot high on 66 minutes, and then forcing Patricio into a sharp stop with a strike on the turn.
De Bruyne was involved in the third goal on 78 minutes, with his cross taking nicks off Doherty and Coady on its way past a helpless Patricio into the bottom corner - an own goal to help the Citizens reach a European high of 99 across all competitions this campaign.
City continue their title defence with a trip to Huddersfield Town on Sunday, and may have to play catch up again with Liverpool in action 24 hours earlier when they host Crystal Palace.
MAN CITY (4-3-3): Ederson; Walker, Stones, Laporte, Danilo; Fernandinho, Bernardo, David Silva (De Bruyne 62'); Sane (Gundogan 74'), Sterling, Jesus (Aguero 76')
WOLVES (3-5-2): Patricio; Bennett, Coady, Boly; Doherty, Dendoncker, Neves, Moutinho (Gibbs-White 72'), Jonny; Jota (Saiss, 59'), Jimenez (Traore, 46') body check tags ::