Captain Vincent Kompany played for the first time since a thigh injury suffered in the Champions League semi-final against Real Madrid in early May, but he went off in the dying seconds as second-half goals by Gael Clichy and Aleix Garcia proved enough.
Guardiola said he would have to await medical reports to find out how serious the injury was.
Swansea, who have now gone four league and cup games without a victory, had their moments as two much-changed teams delivered an entertaining encounter in west Wales, with Gylfi Sigurdsson scoring during second-half injury time.
But the visitors had an extra touch of class about them - helped by second-half substitute Kevin de Bruyne’s introduction - as they moved into the last 16 three days before facing Swansea again, when Premier League points will be at stake.
Guardiola made nine changes from the side that brushed Bournemouth aside 4-0 last Saturday, with only Clichy and Kelechi Iheanacho remaining. Kompany’s return apart, there were also starts for Leroy Sane, Angelino and Garcia, but Sergio Aguero was sidelined as he saw out a three-match ban.
Swansea, meanwhile showed eight changes following a 1-0 defeat at Southampton last time out. Jordi Amat, Jack Cork and Kyle Naughton were retained, while Wales defender Neil Taylor returned following his public show of disapproval after being substituted during the home draw against Chelsea 10 days ago.
City, with Kompany settling quickly and assuredly, made the opening 10 minutes look like a training session as they knocked the ball around with pace and accuracy to leave Swansea pinned inside their own half and fortunate not to fall behind when Angelino powered a shot narrowly wide.
It gave the Swans a wake-up call, though, and they almost went ahead after City goalkeeper Willy Caballero passed the ball from his six-yard area straight to home debutant Borja Baston, whose powerful strike flew inches over the bar.
With Swansea boss Francesco Guidolin cutting an animated figure on the touchline, it was just the response Swansea needed and they continued to push forward as Taylor’s low cross was blocked and forced away for a corner by Kompany.
City soon rediscovered their fluency and it took a superb point-blank save from Swansea goalkeeper Kristoffer Nordfeldt to deny them when he reacted brilliantly after Garcia’s cross was deflected goalwards by Swans defender Mike van der Hoorn.
And it took the visitors just four minutes of the second half to break the deadlock when Kompany began a crisp counter-attack and Angelino’s cross found Clichy, whose shot was deflected over Nordfeldt to make it 1-0.
It underlined the sweeping accuracy of City’s play, and left Swansea needing a quick reply as their opponents showed ominous signs of moving up a gear.
The equaliser almost arrived after John Stones made a hash of clearing from deep, gifting possession to Swansea substitute Sigurdsson, but his shot hit Caballero and City escaped.
And Swansea were then undone again in the 68th minute, with Nordfeldt powerless to prevent Garcia’s shot from flashing past him into the net to end any hopes of a fightback by the home team, despite Sigurdsson’s late consolation when he guided the ball home from Modou Barrow’s cut-back.
Nordfeldt, Rangel, van der Hoorn, Amat, Taylor, Cork (Fer 55), Britton, Naughton (Sigurdsson 61), Fulton, Routledge, Borja Baston (Barrow 75).
Caballero, Zabaleta, Kompany, Stones, Clichy, Tasende (De Bruyne 58), Fernando, Garcia (Adarabioyo 90), Jesus Navas, Sane, Iheanacho (Diaz 80).