The match was six minutes away from going to penalties when Pedro's back-heel gave Hazard a chance, with his shot deflecting off Charlie Daniels and past Artur Boruc.

Bournemouth, who were aiming to reach the semi-final of a major cup competition for the first time in their history, had chances but Callum Wilson shot just wide and Lys Mousset had an effort saved by Kepa Arrizabalaga.

The Cherries, with keeper Boruc joining the attack, had a chance from a free-kick in the 94th minute but shots from Ryan Fraser and Wilson were blocked as the hosts held on.

It means Chelsea boss Maurizio Sarri remains on course for a cup final in his first season in English football.

His side will play Tottenham, 2-0 winners over north London rivals Arsenal, in the semi-finals with the Blues away in the first leg in the week commencing 7 January, before the return at Stamford Bridge two weeks later.

Manchester City, 2018 winners, will face League One side Burton Albion in the other tie.

Chelsea, fourth in the Premier League and eight points behind leaders Liverpool, had the majority of the chances against Bournemouth but Boruc saved efforts from Ross Barkley, Olivier Giroud and Willian in the first half.

The impressive Ruben Loftus-Cheek hit the foot of the post with a fine strike from outside the penalty area before Hazard replaced Barkley in the 61st minute.

The Belgium international shot over the bar and had another attempt from 30 yards well saved by Boruc, before he linked up with Pedro for the game's only goal - his 10th for Chelsea in all competitions this season.

For Bournemouth, they have now lost seven of their past eight games in all competitions, failing to score in their last three matches.

Chelsea in the final four again - the stats

• Chelsea have qualified for the EFL Cup semi-finals in consecutive seasons for the first time since 2007-08.
• Chelsea have won all four of their EFL Cup meetings with Bournemouth, with the last two coming in the quarter-final.
• Eden Hazard has had a hand in 19 goals in all competitions this season (10 goals and nine assists); the most of any Premier League player.
• Chelsea had 12 shots on target against Bournemouth; their most in a game in any competition under Maurizio Sarri.

'Hazard made the difference' - what they said

Chelsea assistant manager Gianfranco Zola said: "The difference was the changes we made. When Pedro and Eden came on, they gave us an extra gear.

"Eden is the type of player who can make a big difference when he comes on, even for 20 minutes.

"He's certainly one of the players who has given this club a lot of satisfaction. He is 27, and hopefully he will stay long with us and become even bigger."

Bournemouth manager Eddie Howe said: "We put in a disciplined defensive display, counter-attacked well and we used the ball well. The result could've been different and I'm so disappointed for those players who gave their all out on the pitch.

"At 0-0 we looked more than capable and had our moments, we just couldn't get that one moment to score.

"Hazard always has a habit of scoring against us, he's a quality player who made the difference.

"We knew we were going to be tested but when you go against the best that's the best way to judge yourselves."