Chelsea will feel aggrieved not to have been awarded a penalty for a Gerard Pique foul on Marcos Alonso when 2-0 down. Alonso also hit the outside of a post with a free-kick and an Antonio Rudiger header hit the bar late on.

But in truth the Blues' hopes were ended when Messi struck after 126 seconds, netting through the legs of the hapless Thibaut Courtois as mistakes proved costly.

Messi's second of the night and 100th Champions League goal was also struck through Courtois' legs, after he had tackled Cesc Fabregas in teeing-up Dembele's sumptuous strike.

With Chelsea adrift of the Champions League qualification places in the Premier League, defeat to Leicester in Sunday's FA Cup quarter-final and then to Tottenham on April 1 could result in a premature departure for head coach Antonio Conte.

Conte's best Champions League performance as a boss remains the quarter-finals with Juventus in 2013, while Barca have now reached the last eight for a record-extending 11th year.

Chelsea were unbeaten in eight games with Barca, but Conte warned they would need to suffer to have any hope of advancing at their hosts' expense.

The Italian also said he would consult his players on tactics for the contest and Eden Hazard was granted his wish after expressing frustration at playing as a 'false nine'.

Hazard, deployed in his customary position on the left of a front three with Olivier Giroud as a central striker, disappointed on a night some saw as his LaLiga audition.

Willian, who gave the Blues the lead at Stamford Bridge, and marauding left wing-back Alonso were Chelsea's most lively attacking threats, but the task was a forlorn one soon after the game ticked into the third minute.

Messi enjoyed good fortune and showed sublime skill to put Barca ahead.

Returning after missing last Saturday's win at Malaga to attend the birth of his third child, Messi stepped by Hazard with ease.

He found Dembele, whose attempted return pass hit Alonso and went to Luis Suarez.

Suarez fed Messi who beat Courtois from wide right of the six-yard box.

Messi, who punished Andreas Christensen's mistake in the first leg, next robbed good friend Fabregas in the centre circle.

He surged by Cesar Azpilicueta, paused and then played the ball across the 18-yard box for Dembele.

⏰ Final whistle at Camp Nou!
FC Barcelona 3-0 Chelsea (4-1)
⚽ Leo #Messi (2) and @Dembouz
👏 Into the quarter-finals!!! Som-hi Barça!!! pic.twitter.com/YSASUs0Ju7

— FC Barcelona (@FCBarcelona) March 14, 2018

The France midfielder made the finish look far easier than it was, firing across goal into the top corner.

Chelsea knew now they needed two unanswered goals.

Alonso shot straight at Marc-Andre ter Stegen and N'Golo Kante fired wide. Fabregas wanted Kante to leave the ball for him - and Conte appeared to be furious that it was not.

Alonso then struck the outside of a post with a free-kick before half-time.

Chelsea came from two goals down with 10 men at the Nou Camp six years ago, but only the most optimistic of Blues supporters could envisage a repeat.

1⃣1⃣ consecutive seasons in the @ChampionsLeague quarter-finals! 👏
✅ 2007/08
✅ 2008/09
✅ 2009/10
✅ 2010/11
✅ 2011/12
✅ 2012/13
✅ 2013/14
✅ 2014/15
✅ 2015/16
✅ 2016/17
✅ 2017/18 pic.twitter.com/qPdVjw6kUu

— FC Barcelona (@FCBarcelona) March 14, 2018

Another Courtois calamity went unpunished as he passed to Suarez before saving the former Liverpool striker's shot.

A brilliant covering tackle by Dembele denied Alonso a shooting chance before Alonso felt he was impeded by Pique.

Conte was furious and Giroud was booked for his protests by referee Damir Skomina, once branded "weak and naive" by Jose Mourinho when the Portuguese was Chelsea boss.

Chelsea's woes deepened as Suarez found Messi, who ghosted by three Chelsea defenders and netted.

Paulinho had a header saved by Courtois and Rudiger headed against the bar at the other end as Chelsea exited and Barca advanced.

- PA