With a league game between the pair on the horizon, this game was never going to see the two teams at full strength and both made nine changes from their line-ups last weekend. Francesco Guidolin kept Jordi Amat and Jack Cork involved, while Gael Clichy and Kelechi Iheanacho were back in action again under Pep Guardiola.
Scoreless but action-packed first half
It was a tight and tense opening at the Liberty Stadium that would eventually burst into life, and that spark came from City's right-hand side. Pablo Zabaleta's cross was fizzed into the feet of Angelino, but the young Spaniard couldn't control his shot and fired wide of the near post on the half volley.
Willy Caballero hadn't looked terribly confident in the early stages and any of his nerves were multiplied by 10 when a poor pass missed Vincent Kompany and fell straight to Borja Baston. He almost marked his first Swansea start with a goal but Caballero reacted quickly to palm his strong shot over the bar.
The lacklustre distribution was a constant theme in the first-half, as the Argentine stopper was less than accurate with the ball at his feet. However, when City did get moving they were causing problems and Mike van der Hoorn's last-ditch tackle was just enough to prevent Leroy Sané from steaming through on goal.
Both sides continued to trade blows but the final ball was sorely lacking. When in behind the Citizens' back-line Wayne Routledge failed to produce a telling cross that was needed to find Borja, while Kristoffer Nordfeldt had to make a superb save to prevent van der Hoorn from putting through his own goal and keep the scores level at the break.
City turn on the style to make it through
All that Swansea hard-work was undone just moments after the break, as City went ahead in the 49th-minute. Some excellent build-up play from the back eventually saw the visitors work the ball forward to Angelino, and he produced a telling pass for Clichy to finish superbly and leave Nordtfelt with no chance.
Guidolin's men didn't let that get them down and they almost equalised around the hour mark when John Stones gave up possession on the edge of his own area. Gylfi Sigurdsson had just come on and his touch was slightly too heavy, allowing Caballero enough to get out and spread himself to make a very good save.
Any steam that the Swans had built up was quickly dashed and in some style. After Jesus Navas picked the ball up on the right, his low cross seemed bound for Iheanacho. He was ready to strike the ball but the young and very impressive Garcia stole in ahead of him to stroke a shot into the far corner from the edge of the area.
Both sides had their chances late on through Kevin de Bruyne and Sigurdsson, and the Icelandic attacker grabbed a late consolation goal for the hosts. He finished well after Moudou Barrow's pass to give them some hope heading into this weekend's fixture. In the end, City were clinical and took their chances to book their place in the next round.