Manchester City advanced to the fourth round of the EFL Cup as second-half goals from Gael Clichy and Aleix Garcia secured a 2-1 victory over Swansea City, although Vincent Kompany appeared to pick up an injury late in the contest.

In a tightly-contested clash at the Liberty Stadium, holders City clicked into gear after the break, Garcia effectively progression with just over 20 minutes remaining, after Clichy's second goal for the club had put Pep Guardiola's side ahead shortly after the restart.

Kompany left the field late in his first competitive appearance since May, substitute Gylfi Sigurdsson having pulled a goal back for Swansea in injury time to ensure a nervy conclusion for the visitors.

The Swans had gone closest to taking the lead prior to the interval on Wednesday – suspect goalkeeping from Willy Caballero almost resulting in a goal for Borja Baston.

But City ultimately made relatively light work of the tie, controlling proceedings for much of the second half as they continued their winning start to Guardiola's tenure.

In the first of two meetings between the sides in the space of three days, it was the visitors who began on the front foot, youngster Angelino drilling wide after connecting with Pablo Zabaleta's cross.

Swansea – winners in 2013 – went close 14 minutes in, record signing Borja pouncing on Caballero's stray pass, but City's goalkeeper atoned for his error with an instinctive save from the Spaniard's venomous strike.

Francesco Guidolin's side continued to press, with only a fine interception from Kompany denying Borja what would have been a simple tap-in from Neil Taylor's cross.

City responded well though, Kristoffer Nordfeldt doing brilliantly to prevent Mike van der Hoorn turning Garcia's delivery into his own goal.

Leroy Sane was the next to test Swansea's resolve but, having latched onto Fernando's clever flick-on, the Germany youngster could only direct a tame half-volley into the grasp of Nordfeldt.

Swansea started brightly following the restart – Borja trying his luck with an acrobatic effort – but it was City who had the lead when they carved open the hosts' defence with a superb counter.

Angelino was the architect, combining sharply with Kelechi Iheanacho before driving forward at pace and picking out Clichy on the cusp of Swansea's area – the full-back's deflected strike evading the grasp of Nordfeldt and nestling into the bottom-left corner.

Guidolin introduced Sigurdsson on the hour, and the Iceland playmaker was almost gifted a goal when John Stones took a heavy touch in City's area, but the former Tottenham man could not make the most of the opportunity.

However, just as Swansea looked to build some momentum, City turned on the style once more, Jesus Navas picking out his compatriot Garcia, who duly prodded in his maiden City goal.

After a period of late pressure, Swansea netted a deserved consolation goal in stoppage time – Sigurdsson nudging home from close range. City, though, will be troubled by the sight of Kompany heading down the tunnel before the final whistle as the visitors held firm to seal progression.