A clever eighth minute free-kick from Kevin De Bruyne and Raheem Sterling's 19th goal of the season were due rewards for first-half dominance and came either side of a scintillating Bernardo Silva strike that was controversially ruled out for offside.
Sane was trying to add to the Championship side's misery before the break, embarking upon a storming counter-attacking run that was halted when an ugly, lunging challenge from Joe Bennett took away his left ankle.
He made way for Sergio Aguero to play his part in a second half gripped by a feeling of formality but attention will now turn to how much damage Sane has suffered as the Premier League leaders prepare for a pivotal phase of their battle for honours on all fronts this season.
With an eye towards Germany's World Cup commitments, the world champions illuminated proceedings by addressing Cardiff over the treatment meted out to Sane and countryman Ilkay Gundogan.
They and Guardiola will hope the cautionary words did not arrive too late, while Bennett belatedly earned his red card with a second caution for hacking down teenage substitute Brahim Diaz.
Hey, @CardiffCityFC. Just letting you know, we have a really important tournament in the summer. Please don't hurt our players. Thanks, #DieMannschaft #inSane — Germany (@DFB_Team_EN) January 28, 2018
Cardiff goalkeeper Neil Ethridge stood firm to repel Gundogan effort in the sixth minute before the midfielder required treatment when Joe Ralls clattered into him on the edge of the box in pursuit of the rebound.
The challenge proved particularly ill-advised as De Bruyne cleverly slotted the resulting free-kick beneath the leaping Cardiff wall and into the net.
Not for the first time in Manchester City colours, Claudio Bravo produced some unsound handling to almost let a speculative Junior Hoillet effort in for an equaliser.
The visitors thought they were 2-0 up in the 25th minute when Silva thundered into the top corner, although Leroy Sane was ruled to be in an offside position – replays suggested he was level – and obscuring the view of Ethridge, who was rendered relatively helpless by the velocity of the strike.
The decision went down badly with Guardiola, who remained visibly dissatisfied on the sidelines when referee Lee Mason unsuccessfully told him to calm down.
Silva was at the heart of things once more when it came to improving his manager's mood in the 38th minute, with a sweetly struck left-wing cross dispatched beyond Ethridge despite Sterling's header not being one from the textbook.
Aguero's introduction in place of the stricken Sane did not stop Manchester City's attack from functioning smoothly, with a magnificent tackle by Cardiff captain Sean Morrison required to deny Sterling the seeming formality of a third after the England winger rounded Ethridge.
Kenneth Zohore snatched at a rare opening for the hosts, firing over the near post after Paterson got the better of Vincent Kompany with a flick on.
Guardiola's men had dropped their intensity to dangerously low levels and Cardiff sensed a route back into the contest, with substitute Anthony Pilkington almost making an immediate impact from Morrison's set-piece knockdown before Hoilett's sweetly struck 25-yarder rippled the top of the netting.
Manchester City rode out some discomfort before the excellent Silva and Danilo almost added gloss to the scoreline, meaning Guardiola will have at least a few more weeks to be irritated by quadruple talk. Bennett, on the other hand, might wish to undertake some quiet reflection.
Key Opta facts:
- Following Kevin De Bruyne’s opener, Manchester City now have five players to have scored at least 10 goals in all competitions this season, more than any other English league side (Sergio Aguero, Raheem Sterling, Leroy Sane, Gabriel Jesus and De Bruyne).
- Of his 10 goals this season, De Bruyne has now scored six from outside the box, at least two more than any other Premier League player.
- Cardiff City have progressed just once from their last 11 FA Cup ties against sides from a higher division, last beating then Premier League side Middlesbrough, back in 2008.
- As a manager, Pep Guardiola has lost just once in 22 meetings with sides from a lower division (W19 D2), with that sole defeat coming in a Copa Del Rey match against Real Betis back in January 2011.
- Sterling's goal was his first headed effort in any club competition since Boxing Day 2015, in a Premier League game against Sunderland.