The irrepressible Argentine, along with strike partners Luis Suarez and Neymar, had been subdued for most of the last 16, first-leg tie but came alive late on, clinically finishing off a lightning counter-attack and then dispatching a penalty.
“They are 95 percent through to the quarter-finals certainly,” Arsenal manager Arsene Wenger, whose side had defended solidly for 71 minutes until crumbling, told reporters.
“It’s a shame we didn’t get any satisfaction because we put everything into it.”
Luis Enrique’s Barca side extended their unbeaten run to 33 matches and, barring something extraordinary in the return at the Nou Camp next month, will take their place in the last eight for the ninth season in a row.
“I liked everything we did tonight,” the Spaniard told reporters.
Messi has proved a thorn in Arsenal’s side on each of the last two occasions the teams have met in the Champions League.
In 2010 he scored four times in the last 16 second leg to send Barca through and a year later he struck twice in a 3-1 win in Spain after Arsenal had edged the first leg.
Messi, Suarez and Neymar had scored 91 goals in all competitions this season heading into Tuesday’s game but none of the feared trident managed an effort on target in the first half as Arsenal’s fans cranked up the decibel levels.
Arsenal were patient and should have gone ahead midway through the first half when Hector Bellerin’s scuffed shot fell for Alex Oxlade-Chamberlain but he scooped his effort straight into the arms of keeper Marc-Andre ter Stegen.
The Catalans began to move through the gears though and either side of halftime wasted two glorious chances.
Suarez, who has 41 goals in all competitions this term, headed Dani Alves’s dinked cross wide with the goal gaping before Neymar was denied by goalkeeper Petr Cech after being played in by Andres Iniesta.
Starved of the ball for long periods, Arsenal still posed a threat and Ter Stegen did well to keep out Olivier Giroud’s close-range header from a Mesut Ozil cross.
Arsenal grew in belief but it cost them dear as they committed players forward and got stung on the break.
With 19 minutes left they lost the ball near Barca’s goal and Suarez and Neymar combined in devastating fashion, the Brazilian unselfishly picking out Messi who steadied himself before beating Cech for the first time in his career.
Suarez then hit the post when he should have scored before Messi scored again, this time with a calmly struck penalty after substitute Mathieu Flamini had tripped him.