The signs looked ominous for the relegation-threatened visitors when City came flying out of the blocks and opened the scoring after less than six minutes through man of the match Kevin De Bruyne.
However, it took Pep Guardiola's side until the 44th minute to double their advantage through Leroy Sane, and despite a string of chances and overwhelming dominance they failed to add a third goal in the second half.
City nonetheless climb a point clear of Liverpool at least until the Reds face Southampton on Friday, whereas Cardiff remain five points from safety with just six games of their season to go.
The hosts were without the likes of Sergio Aguero, Raheem Sterling and David Silva, but that did not prevent them from making a quick start to the match and they came close to breaking the deadlock inside 30 seconds.
De Bruyne advanced into the box from the right flank and worked space to put a low ball into the area which flashed across the six-yard box and was inches too far in front of Gabriel Jesus.
That set the tone for the opening exchanges as Man City cut Cardiff open almost at will, and it took a smart reaction save from Neil Etheridge to keep out Riyad Mahrez's deflected low drive after four minutes - the first of nine stops the Cardiff keeper would make.
The champions would not have to wait much longer for their opener, though, and it came in unorthodox fashion as the dangerous De Bruyne picked out the roof of the net from a seemingly impossible angle, beating Etheridge at his near post after the Cardiff keeper had wrongly anticipated a cross into the middle.
Even after only six minutes there was a feeling of inevitability about the goal, and at that stage it looked as though it would be a question of how many City would score with Sane testing the keeper again and Jesus firing over before the 15-minute mark.
Cardiff did begin to stem the tide of chances as the first half wore on, but Man City occasionally still broke through and De Bruyne continued to be the chief creator, firing a low ball into the box shortly before the half-hour mark which was turned inches wide by a mixture of Jesus and Bruno Ecuele Manga.
The hosts were forced to settle for long-range efforts during a particularly stubborn spell from Cardiff, but they should have doubled their advantage five minutes before the interval when De Bruyne led a lightning counter-attack before giving the ball to Jesus, who failed to beat Etheridge at the near post when De Bruyne wanted a return pass inside.
Man City did finally break Cardiff's resolve for a second time just before half time, though, as Mahrez stood a ball up to the back post for Jesus to cleverly chest down to Sane, who lashed a crisp first-time half-volley into the bottom far corner.
It was much the same pattern of Man City dominance in the second half too, and Phil Foden almost marked his first Premier League start with a goal when he latched on to Fernandinho's pass before being thwarted by Etheridge six minutes after the restart.
Fernandinho glanced a header of his own wide shortly afterwards, while Aymeric Laporte and De Bruyne may also feel they should have done better with efforts that failed to hit the target either side of the hour mark.
Guardiola's side did soon up the tempo again, though, and they laid siege to the Cardiff goal during a six-minute spell which somehow did not end up with a third goal.
Etheridge was forced into five saves during that period alone - including particularly good ones to deny Laporte, Sane and Foden - while Sean Morrison put the ball inches past his own goal.
Even when City did find a way past Etheridge the woodwork came to Cardiff's rescue, with Foden clattering a smart volley against the post before Fernandinho could only bundle the rebound wide.
It took until the 74th minute for Cardiff to finally register their one and only shot on target as Ederson comfortably gathered a tame strike from Oumar Niasse - a moment the travelling Cardiff supporters celebrated like a goal.
It was only the second shot on target Man City had allowed in their last four league games, though, and the first they had faced since March 9 as they enjoyed another dominant display.
Jesus squandered another chance for an elusive third goal 12 minutes from time when he tried to be too elaborate with his finish, and City were almost handed a late scare as a hitherto toothless Cardiff threatened to punish their profligacy.
The visitors hit City on the break with Nathaniel Mendez-Laing and Niasse combining to eliminate the last defender from the equation, but Niasse then took too long over his finish and allowed Ederson to come out an smother the ball when Cardiff should have scored.
It was a rare moment of defensive vulnerability for City as they cruised to a 13th successive victory across all competitions to pile the pressure back on Liverpool during a weekend which sees the champions turn their attention to the FA Cup element of a potential quadruple.
MAN CITY (4-3-3): Ederson; Danilo, Stones, Laporte, Zinchenko (Walker 19'); De Bruyne, Fernandinho, Foden; Mahrez, Jesus, Sane
CARDIFF (4-4-1-1): Etheridge; Peltier, Morrison, Ecuele Manga, Bennett; J Murphy (Mendez-Laing 60'), Gunnarsson (Bacuna 81'), Ralls, Hoilett; Camarasa (Reid 83'); Niasse body check tags ::