Match ends, Chelsea 2, Bournemouth 1.
Alvaro Morata scored an injury-time winner as Chelsea beat Bournemouth to reach the Carabao Cup semi-finals, with boss Antonio Conte relieved to avoid a "dangerous" period of extra-time.
Willian opened the scoring, capping a fine team move which resulted in Cesc Fabregas squaring for the Brazilian to tap home.
Bournemouth thought they had forced extra-time when Dan Gosling curled home from the edge of the box in the final minute after being picked out by Jordon Ibe.
But substitute Morata sent Conte's team into the last four when he finished from Eden Hazard's backheel.
Chelsea will play Arsenal in the semi-finals, hosting the first leg in the week commencing 8 January. The second leg is two weeks later. Manchester City play Bristol City in the other tie.
Conte said: "To play 30 minutes more would have been a bit dangerous. We had a great reaction. It's not simple to concede a goal in the last minute of the game.
"When you have this reaction, it means you have players with great character and heart."
Chelsea fringe players win - but don't shine
All seven Premier League teams in the quarter-finals made wholesale changes, an average of 8.3 per side. And Chelsea were no exception, making eight switches from Saturday's 1-0 win over Southampton.
The Blues will be delighted to be in the semi-finals of a cup they have won five times, although an experienced team of fringe players did not do much to stake a claim for a Premier League spot. Teenager Ethan Ampadu, one of only two players in the team aged 21 or under, was impressive at centre-back, though.
Striker Michy Batshuayi and Kenedy were both involved in the goal for Willian, one of the few Premier League regulars in the team, and both recalled players missed chances.
Batshuayi was denied by a couple of last-ditch Steve Cook interceptions in the first half, with left wing-back Kenedy screwing a shot well wide after winning the ball from Adam Smith on the halfway line.
The Blues sat back in the second half, and invited pressure from Bournemouth.
Conte was obviously not too impressed with what he saw, and brought on Hazard, Tiemoue Bakayoko and then Morata in a bid to turn the tide.
And it was his star players who sent them into the last four. Moments after Bournemouth's equaliser, Morata let a ball forward run to Hazard and moved towards the penalty spot, where he received the Belgian's backheel before firing past Artur Boruc.
Conte said: "Last season, we were eliminated in the fourth round by West Ham. This season we must be happy with this achievement in reaching the semi-final of one of the two cups in England.
"It's great for us, especially because we reached the semi-final with a lot of rotations. From the first game against Nottingham Forest I made a lot of rotations, and for this reason I am very happy.
"I had good responses from my players. In this cup, they showed they are very professional. I hope this game also improves the physical condition especially for the players who had injuries and who are not playing with regularity. It means we are working very well."
Bournemouth give it a good go - but can now focus on league
Perhaps if Bournemouth were comfortable in mid-table, they could have given the EFL Cup a real crack this season. But the Cherries sit just one point above the relegation zone - and manager Eddie Howe decided to rest players with the festive fixtures in mind.
Jermain Defoe was one of the four players to keep his place from the 4-0 defeat by Liverpool, but hobbled off following Ampadu's mis-timed first-minute challenge. Howe confirmed after the game that the veteran striker has suspected ankle ligament damage.
The Cherries offered little in the first half - although Lyn Mousset headed at goalkeeper Willy Caballero and Ibe shot wide after Willian had mistakenly waited for a free-kick to be awarded.
They caused more problems after the break, with Mousset having a shot deflected for a corner, Lewis Cook firing over and Ibe firing wide after Callum Wilson found him following a slick team move.
Bournemouth deserved their equaliser when Gosling scored from 20 yards - but their joy lasted precisely 75 seconds with Morata scoring a late, late winner.
Howe said the defeat was "heartbreaking".
"The players gave everything," said the Cherries boss. "In the second half, we had waves of attack and we scored, but the last part of the game is bitterly disappointing.
"I think we're experienced enough to know, but it's just one of those things. The most positive thing is that our players continued to dominate the ball."
Analysis - 'there would have been questions had Chelsea lost'
Former Chelsea goalkeeper Mark Schwarzer on BBC Radio 5 live sports extra
Maybe Bournemouth thought they were going to extra-time and switched off a little bit. But Chelsea had other ideas. When you have Eden Hazard, anything can happen.
Bournemouth were really good in the second half and deserved their equaliser; they put Chelsea under a lot pressure. Hazard and Morata came through for them.
To win a cup, whichever one it is, is important. The weight of expectation is enormous at Chelsea. You're expected to win every trophy. There would have been questions asked had they lost. Chelsea aren't used to losing.
The problem for Bournemouth is they've shown glimpses like that this season but they can't maintain it. In the second 45 minutes, they were exceptional - rejuvenated, a different side. They had to throw everything at it and they did. Now it's over with they've got to put it to bed and focus on the Premier League.
Man of the match - Ethan Ampadu (Chelsea)
Conte praised Wales international Ampadu, a summer signing from Exeter.
"After one minute and 40 seconds the referee decided to book a player who is 17 years old. Ampadu played the whole game with this problem. That's not easy. He had to play 93 minutes with this danger, but he showed great maturity and personality.
"I have spoken about this player before in an enthusiastic way. Despite his young age, he is showing great maturity.
"He deserved to play tonight, he deserved to play against Everton, he deserved to play his first league game against Huddersfield. Now he has to stay calm. Maybe next game he goes to play for the youth team, I don't know. This player is very humble. He could have a great future, but he has to continue in this way."
Match stats - four shots on target, three goals
- Chelsea have reached the EFL Cup semi-finals for the 13th time - they have progressed to the final on four the last five occasions they have reached this stage.
- There were just four shots on target in the entire match, with three of them being scored - the two in the 90th and 91st minute were the only shots on target in the second half.
- Willian has scored in both of his EFL Cup appearances this season, after failing to score in each of his first nine in the competition.
- Cesc Fabregas recorded his 52nd assist in all competitions for Chelsea, at least 20 more than any other player at the club since he signed in 2014-15.
Chelsea go to Everton in the Premier League on Saturday at 12:30 GMT, although they will be without Morata, whose booking for celebrating his goal means a one-game suspension.
Bournemouth are away to unbeaten leaders Manchester City at 15:00.
- 44AmpaduBooked at 2mins
- 21ZappacostaBooked at 62mins
- 4FàbregasBooked at 39mins
- 22WillianSubstituted forE Hazardat 61'minutes
- 23BatshuayiSubstituted forMorataat 73'minutesBooked at 90mins
- 11PedroSubstituted forBakayokoat 61'minutes
- 10E Hazard
- 37dos Reis Carvalho
- 15A SmithBooked at 82mins
- 2FrancisBooked at 76mins
- 3S Cook
- 42SimpsonBooked at 72mins
- 8ArterSubstituted forL Cookat 74'minutes
- 4GoslingBooked at 90mins
- 18DefoeSubstituted forIbeat 17'minutes
- 31MoussetSubstituted forWilsonat 71'minutes
- 16L Cook
- Lee Mason
- Shots on Target
Second Half ends, Chelsea 2, Bournemouth 1.
Willy Caballero (Chelsea) wins a free kick in the defensive half.
Foul by Artur Boruc (Bournemouth).
Corner, Bournemouth. Conceded by Davide Zappacosta.
Attempt blocked. Ryan Fraser (Bournemouth) left footed shot from the left side of the box is blocked.
Foul by Davide Zappacosta (Chelsea).
Ryan Fraser (Bournemouth) wins a free kick in the defensive half.
Álvaro Morata (Chelsea) is shown the yellow card for excessive celebration.
Goal! Chelsea 2, Bournemouth 1. Álvaro Morata (Chelsea) right footed shot from the centre of the box to the centre of the goal. Assisted by Eden Hazard.
Dan Gosling (Bournemouth) is shown the yellow card for excessive celebration.
Goal! Chelsea 1, Bournemouth 1. Dan Gosling (Bournemouth) right footed shot from outside the box to the bottom right corner. Assisted by Jordon Ibe.
Offside, Chelsea. Kenedy tries a through ball, but Eden Hazard is caught offside.
Foul by Lewis Cook (Bournemouth).
Ethan Ampadu (Chelsea) wins a free kick in the defensive half.
Corner, Bournemouth. Conceded by Davide Zappacosta.
Davide Zappacosta (Chelsea) wins a free kick in the defensive half.
Foul by Callum Wilson (Bournemouth).
Foul by Álvaro Morata (Chelsea).
Ryan Fraser (Bournemouth) wins a free kick on the left wing.