The club-record signing was introduced from the bench and netted twice in the second half to round off the Citizens' scoring, following first-half goals from Sergio Aguero, Bernardo Silva and Ilkay Gundogan.
A first top-flight victory at Cardiff in seven attempts keeps Man City within two points of Liverpool at the top of the division, while the Bluebirds are still winless and are now just one place off the foot of the table.
Man City were made to toil by their opponents prior to the floodgates opening, as they failed to register a shot of any note prior to Aguero's opener 32 minutes in.
Man City then started to turn their possession into chances, coming close through Gundogan's skied half-volley from inside the box, moments before Aguero's vital opener.
Gundogan's reverse pass was gathered by Bernardo, who in turn squared for Aguero to tuck out of Neil Etheridge's reach on the striker's landmark 300th outing in Man City colours.
Bernardo added the second himself three minutes later with a flicked header into the far corner, although it looked more like an intended pass towards the back post than an effort at goal.
Danny Ward's tame attempt down the middle for Ederson to collect was the best Cardiff had to offer in a first half that got progressively worse, as Gundogan slammed home a third into the top corner after exchanging passes with Raheem Sterling.
Cardiff, fortunate to still have a full complement of players for the second half following Joe Ralls's shin-high challenge on Gundogan, were dealt a further blow a minute after the restart as Peltier landed awkwardly and was stretchered off.
If not for a couple of Etheridge stops to deny Aguero the visitors could have been even further ahead by the hour, while Sane was guilty of missing a sitter from close range.
The fourth goal of the afternoon did arrive shortly after, though, courtesy of a Mahrez tap-in following some good play from Sterling and Gundogan in the build-up.
Bernardo should have added to that tally when picked out in a good position 10 yards from goal, only for his shot to deflect over the bar, and Mahrez was thwarted by Etheridge at his near post late on.
There was to be no stopping Mahrez in the final minute of normal time, however, as he picked out the bottom corner following a poor piece of defensive play from Bruno Ecuele Manga to compound Cardiff's misery.
CARDIFF CITY (4-4-2): Etheridge; Peltier (Richards 51'), Manga, Morrison, Cunningham; Camarasa, Arter, Ralls, Hoilett (Murphy 75'); Ward (Zohore 63'), Reid
MANCHESTER CITY (4-2-3-1): Ederson; Walker, Laporte, Otamendi, Delph; Fernandinho (Stones 74'), Gundogan (Foden 69'); Sterling, B.Silva, Sane; Aguero (Mahrez 61')