Barcelona advanced 4-1 on aggregate following a 1-1 first-leg draw in London.
Messi beat Thibaut Courtois with two strikes between the Chelsea goalkeeper's legs from very tight angles on the side of the box. He struck the opener three minutes into the match and took Barcelona's third goal in the 63rd.
Barcelona goalkeeper Marc-Andre ter Stegen jumps to punch the ball away during the Champions League round of sixteen second leg soccer match between FC Barcelona and Chelsea at the Camp Nou stadium in Barcelona, Spain, Wednesday, March 14, 2018. (AP Photo/Manu Fernandez)
But the most dazzling moment from the Argentina forward, who returned from missing one match for the birth of his third son on Saturday, came when he helped Ousmane Dembele score his first goal for Barcelona after he stole the ball from former Barcelona teammate Cesc Fabregas and darted past two would-be tacklers in the 20th.
Barcelona remained unbeaten in 25 straight Champions League matches at Camp Nou, a run that dates back to 2013. The hosts also stayed in contention for a rare treble of titles. They lead the Spanish league and have reached the final of the Copa del Rey.
Chelsea will now have to focus on finishing in the top four in the Premier League to return to tournament. It is currently in fifth place.
Chelsea's Marcos Alonso falls down between Barcelona's Gerard Pique, left, and Sergi Roberto during the Champions League round of sixteen second leg soccer match between FC Barcelona and Chelsea at the Camp Nou stadium in Barcelona, Spain, Wednesday, March 14, 2018. (AP Photo/Manu Fernandez)
Also on Wednesday, Bayern Munich won 3-1 at Besiktas to advance 8-1 on aggregate. Thiago Alcantara and Sandro Wagner scored for Bayern and Gokhan Gonul's added an own goal.
Barcelona coach Ernesto Valverde chose to start Dembele over midfielder Paulinho, who played the match in London which Chelsea largely dictated. The decision proved the right one when Messi linked up with the young winger to double the lead.
Andres Iniesta returned from a muscle injury in his right leg suffered 10 days ago to play the first hour for Barcelona, before he was substituted by Paulinho with the win in hand.
Chelsea's Olivier Giroud reacts after Barcelona's Lionel Messi scored his side's third goal during the Champions League round of sixteen second leg soccer match between FC Barcelona and Chelsea at the Camp Nou stadium in Barcelona, Spain, Wednesday, March 14, 2018. (AP Photo/Manu Fernandez)
Chelsea boss Antonio Conte looked to repeat the team's relative success at frustrating Barcelona's attack from the first leg with its back line of five defenders.
But Messi needed very little to poke a hole in Chelsea's wall.
Barcelona's all-time leading scorer started an attacak with a pass meant for Dembele that was twice deflected before Luis Suarez deftly flicked it back to Messi.
Barcelona's Ousmane Dembele, left, celebrates with Lionel Messi after scoring his side's second goal during the Champions League round of sixteen second leg soccer match between FC Barcelona and Chelsea at the Camp Nou stadium in Barcelona, Spain, Wednesday, March 14, 2018. (AP Photo/Manu Fernandez)
The Argentine targeted the only gap available: the slot in-between the legs of Courtois.
The second came after Messi swooped in to steal the ball from Fabregas in midfield and charged toward the box. After letting Suarez draw the remaining defenders to him, Messi passed across for Dembele to drive a rising shot over Courtois.
Dembele's first goal for Barcelona came in his 12th appearance for the club. The goal could represent a breakthrough for the 20-year-old France winger, who had been hesitant and error-prone in his previous games after recovering from two injuries since his move from Borussia Dortmund that could reach 147 million euros (about $173 million).
Barcelona's Lionel Messi celebrates after scoring his side's third goal during the Champions League round of sixteen second leg soccer match between FC Barcelona and Chelsea at the Camp Nou stadium in Barcelona, Spain, Wednesday, March 14, 2018. (AP Photo/Emilio Morenatti)
Despite getting nothing from striker Olivier Giroud, Chelsea continued to press for a goal and came closest near the end of the first half.
Willian and Eden Hazard both drew saves from goalie Marc-Andre ter Stegen and defender Samuel Umtiti before Marcos Alonso then sent a free kick off the post in injury time, adding his near miss to Willian's two shots off the woodwork from the first leg.
Dembele also contributed in defense when he hustled back to make a clean tackle of Alonso when he was preparing to shot from close early in the second half.
Barcelona's Lionel Messi celebrates after scoring his side's third goal during the Champions League round of sixteen second leg soccer match between FC Barcelona and Chelsea at the Camp Nou stadium in Barcelona, Spain, Wednesday, March 14, 2018. (AP Photo/Emilio Morenatti)
Messi made sure of the victory when he received a pass from Suarez and sped around a group of three defenders before humbling Courtois with a second strike between the legs.
Antonio Rudiger came closest to a consolation goal for Chelsea, but his header hit the crossbar in the 90th minute.