After unfurling a banner showing the words "God Save The King" before kick-off, Barca's fans were celebrating after just 129 seconds at the Camp Nou as Messi found the net before Chelsea had even made a pass.
He then teed up Ousmane Dembele to double Barca's lead in the second leg of the last-16 clash before registering a century of Champions League goals on his 123rd appearance to complete a 3-0 victory, 4-1 on aggregate.
Messi becomes only the second player to reach the milestone in Europe's premier tournament, following Real Madrid's Cristiano Ronaldo, who has 117 goals in 152 games.
"He knows in certain moments the stars have to come out," Barcelona coach Ernesto Valverde said. "We enjoy him. We're lucky enough to be seeing something that will go down in history."
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By the end, the Argentinian's scintillating breakaway in the build-up to Dembele's first Barcelona goal had become little more than a footnote to what was another Messi masterclass.
"I think that a fantastic player moved the final result," said Chelsea manager Antonio Conte. "In these two legs, he scored three goals, he made an assist for Dembele to score a goal. It's a pity."
It also caps a remarkable five days for the 30-year-old, who sat out Saturday's La Liga win over Malaga to attend to the birth of his third child.
Chelsea, in touch after the 1-1 draw at Stamford Bridge, were therefore unfortunate enough to encounter the striker fresh, free and at his frighteningly brilliant best.
At the finish, Conte left the field with his arm around the forward, perhaps with nothing to add but congratulations.
"I think when you have the opportunity to make great compliment to Messi, I think it's right," added Conte. "It's right to recognise a super, super, super top player."
Conte's team had chances, particularly in the first half, but the sense was once Barcelona were in front they were content to sit back and counter.
Chelsea hit the woodwork twice and claimed for a penalty when Alonso was brought down by Gerard Pique.
"If you watch the game you can see the final result is unfair," said Conte. "Over the two legs we hit the post four times. This is very strange."
With Manchester United dumped out by Sevilla and Tottenham outmanoeuvred by Juventus, Chelsea's exit means for all the talk of a Premier League resurgence, Liverpool and Manchester City are its only two representatives in the quarter-finals.
Spain have three, after Real saw off the challenge of Paris Saint-Germain.
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