Liam Delap scored a debut stunner but holders Manchester City needed a late Phil Foden winner to see off Championship side Bournemouth 2-1 in the Carabao Cup.
Delap, the 17-year-old son of former Stoke midfielder Rory, put the holders ahead in style in their third-round tie at the Etihad Stadium but they were immediately pegged back by Sam Surridge.
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City brought Kevin De Bruyne and Raheem Sterling off the bench in the latter stages and they eventually snatched victory on 75 minutes when Foden struck after Riyad Mahrez hit the post.
Pep Guardiola's side, who are bidding for a record-equalling eighth League Cup win and a fourth in succession, will now travel to Burnley in the fourth round next week.
How City class swept Cherries aside
Looking ahead to Sunday's clash with Leicester, City boss Guardiola made eight changes from the side which opened the campaign with victory at Wolves on Monday. His selections included handing debuts to the impressive striker Delap and American goalkeeper Zack Steffen.
Tommy Doyle and Taylor Harwood-Bellis were also given opportunities but it proved a sad night for 19-year-old Adrian Bernabe, who was carried off injured before half-time.
City's youthful side threatened early on as Ferran Torres, making his first start since his summer move from Valencia, and Mahrez forced saves from Mark Travers.
They then took the lead on 18 minutes as Foden slid Delap through on goal with a fine through-ball. The teenager took the ball in his stride and swept a left-footed shot into the top corner from just inside the box.
It was a moment to savour for the youngster but City's lead proved short-lived as the Cherries responded within four minutes. Surridge was given too much space to turn in the box and buried a low shot past Steffen.
Both sides suffered an injury blow before half-time as Bournemouth's Lloyd Kelly and then Bernabe were forced off. Bernabe's problem looked particularly serious and City boss Pep Guardiola dashed over to console the youngster as he was wheeled past the technical area on a stretcher.
City tried to push after the break but Bournemouth held firm and grew in confidence. Surridge was twice denied as first Harwood-Bellis blocked a shot and then Steffen raced out of his area to cut short another charge.
Guardiola decided to up the tempo just after the hour by summoning De Bruyne and Sterling from the bench. The pressure on the Bournemouth back line increased and City eventually made their breakthrough.
Mahrez struck the woodwork with a low shot and Foden was in the right place to tuck home the rebound. City went in search of more and Delap's enthusiasm got the better of him as he crashed into Cherries goalkeeper Travers, collecting a booking for the late challenge.
City had a late scare when De Bruyne went down after a blow to the head but he was able to complete the game.
What the managers said
Manchester City manager Pep Guardiola said: "It was a young team. All of them played incredibly. It was good for us. The opponent was tough. I felt we deserved the victory. In the second half we were much better.
"We see him [Delap] in training and he scores a lot. He's a striker we don't have - strong and good in the air. We have a lot of confidence with him for the future.
Bournemouth manager Jason Tindall said: "We are disappointed we have gone out of the cup but I'm pleased with the performance. We were brave and good in possession and caused Manchester City a few problems.
"It was testament to how we did in the game they brought on the likes of De Bruyne and Sterling. I didn't feel they created too many clear-cut opportunities and felt we were a threat. I'm disappointed with losing the game.
"I felt it was a late challenge [from Delap on Travers], a bad challenge, a heart-in-mouth-moment to see Trav stay down for some time. I was delighted he wasn't hurt but it was difficult to see from where I was in terms of what card it should be."
What's next?
Manchester City host Leicester on Super Sunday at 4.30pm - live on Sky Sports Premier League - while Bournemouth host Norwich in the Sky Bet Championship on Sunday at 4pm.