Manchester City will continue to fight on four fronts after victory against Oxford United earned Pep Guardiola’s side a mouthwatering match-up against Manchester United in the Carabao Cup semi-finals.

City had to battle for the win and are digging their heels in over Mikel Arteta, whose presence here dominated the discourse before and after this entertaining contest.

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Arsenal expect to appoint Arteta as their next manager but Guardiola was prickly when asked about his assistant’s future, with City furious at the club’s conduct, insisting they have not made a formal approach for the Spaniard.

City, who have won this competition the past two years, dominated the first half but Oxford made an experimental visiting side sweat in the second half.

Oxford had 18 shots – the most City have faced under Guardiola – but could not wrestle their way back into the game after a second-half Raheem Sterling double earned the visitors some breathing space. Sterling, who wore the captain’s armband and operated as a striker here as Guardiola rested eight players, displayed a poacher’s instinct, twice applying the finishing touches inside the six-yard box after Matty Taylor cancelled out João Cancelo’s opener immediately after the restart.

Oxford asked questions but City, who have not lost in this competition since defeat to Manchester United in October 2016, held on to maintain their hopes of defending the trophy.

The cover of the match-day programme was dedicated to Jim Smith, the former Oxford manager, who last week died at the age of 79. Before kick-off there was a warm minute’s applause and the former Manchester City forward Mike Summerbee and the former Oxford striker Jeremy Charles placed wreaths in tribute to Smith behind the East Stand goal.

This was a meeting between two of the country’s biggest entertainers – only West Brom and Peterborough have outscored Oxford in the Football League this season – and Karl Robinson’s side tested a youthful City defence after the break having been kept at arm’s length for much of the first half. “Nervous is not the word but they pushed a lot, they played so well, created lots of chances,” Guardiola said of Oxford. “But we are in the semi‑finals for the third season in a row.”

Quick guide Carabao Cup draw throws up Manchester derby Show Hide Manchester City will need to beat rivals Manchester United over two legs if they are to defend the Carabao Cup trophy this season. City and United, who beat their neighbours in the Premier League on 7 December, were paired together in the semi-final draw. The other last-four clash is also a derby, with Leicester taking on midlands rivals Aston Villa. City have won the trophy in three of the last four seasons, with United not making the showpiece of this competition since 2017, when they left it late to beat Southampton. Leicester have reached the semis for the first time in 19 years, when they went on to beat Tranmere in the final, while Villa were last at this stage in 2013, losing to Bradford. The first legs will be played in the week beginning 6 January, with the return fixtures taking place three weeks later. On drawing rivals City in the last four, United boss Ole Gunnar Solskjaer told Sky Sports: "We always want to win trophies and we want to win games. "We've got a nice little draw coming up so it'll be exciting times coming up. I don't think anything is written in the stars. We just work hard and you take what you get and you do the best out of it."

Rodri, one of only three survivors from the starting lineup at the Emirates Stadium on Sunday, was instrumental throughout and Cancelo and Riyad Mahrez combined neatly down the right flank but City spent much of the second half repelling Oxford attacks.

The celebrations after Sterling struck were low-key – business as usual had been restored – and City had work to do to fend off Oxford, who sensed an air of vulnerability.

“We cannot play like that and not build on it – we were horrendous on Saturday [at MK Dons] – we have to find some consistency,” said Robinson, the Oxford manager, whose side return to League One action against Wycombe this weekend.

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Tariqe Fosu was a livewire, while Cameron Brannagan, who spent 16 years on the books at Liverpool, showed a touch of class in midfield and Rob Dickie, the Oxford captain, displayed composure in defence in a difficult environment, with a swirling wind making life difficult for both teams.

“They were really tough conditions – winter is here,” Guardiola said. “They [Oxford] are a top side. Last season [in City’s 3-0 cup win] they played good and I think this season they played better, so maybe next season we will be back. Cup competitions away in this period are always really, really tough.”

City were in cruise control after Cancelo’s opener, stroking the ball around for fun, successfully sapping Oxford’s energy and belief but the hosts roused themselves immediately after the interval, striking within 21 seconds of the restart.

Oxford rippled Claudio Bravo’s net without City getting their mitts on the ball; from kick-off a recharged Oxford piled forward down the right, with Shandon Baptiste’s quick thinking outwitting a green City backline, comprising the 17-year-old Taylor Harwood‑Bellis and the 18-year-old Eric García.

After being fouled by García, Baptiste’s free-kick released Taylor, the Bristol City loanee, who turned inside Harwood-Bellis before sending a left-foot effort beyond Bravo. Oxford’s joy may have been short-lived – City retook the lead four minutes later – but they gave the Premier League champions a fright.

“To take them on at the game they are best in the world at is crazy, stupid but I didn’t want us to roll over and not lay a glove on them,” said Robinson.

“If Jim is looking somewhere, I think he would be a very proud man. He built a club with next to nothing and put us in a position at the top of English football.

“Our love and thoughts are with his family and we’ll dedicate that performance to him. It had everything he believed in – heart, desire and entertainment – and hopefully we’ve done him proud.”