The Gunners had given themselves a fighting chance in their last-16 second leg clash in the Nou Camp when Sergio Busquets' own goal (53) had cancelled out Messi's brilliant opener (45).
But once Robin van Persie saw red for a second bookable offence (56), the Gunners were always on the backfoot and goals from Xavi (69) and Messi (penalty, 71) ended their Champions League hopes for another season.
Arsenal, though, will be left with a sense of injustice after seeing van Persie controversially sent off in an incident that swung the game in Barcelona's favour.
The Dutchman was a shock inclusion for the Gunners, who led 2-1 from the first leg, having recovered quicker than expected from the knee injury he sustained in the Carling Cup final.
Van Persie had already been booked in the first half and was shown a second yellow card for lashing the ball towards goal after a marginal offside call which the Arsenal striker claimed he could not hear.
Barcelona took full advantage, with Xavi and then Messi's penalty putting the tie beyond Arsene Wenger's men, who were left to reflect on what might have been and must now regroup for Saturday's FA Cup quarter-final at Premier League title rivals Manchester United.
As expected, Barcelona went on the offensive from kick-off, cheered on by a passionate 95,000-strong crowd in the Nou Camp.
Laurent Koscielny made an important early block on Pedro and when the visitors did get possession, they were greeted by a cacophony of deafening whistles.
Koscielny and Jack Wilshere combined to deny Messi after, in a sign of things to come, Arsenal again gave away possession far too cheaply.
The Gunners were forced into a change on 16 minutes when goalkeeper Wojciech Szczesny had to be replaced by Manuel Almunia after injuring his left hand making a routine save from Daniel Alves' long-range free-kick.
Barcelona continued to press Arsenal back, with Johan Djourou producing a superb saving tackle to deny Xavi with Pedro drilling the loose ball over the crossbar.
Barcelona then almost fluked an opening goal on 35 minutes when a curled cross from left-back Adriano struck the outside of the near post.
Tempers boiled over when Wilshere went to ground as he stretched for a loose ball at the edge of the Barcelona penalty area, the home players claiming a dive which led to van Persie and former Liverpool midfielder Javier Mascherano squaring up before calm was eventually restored.
Van Persie had not calmed down and picked up a needless yellow card on the stroke of half-time for barging Alves over.
Fabregas, returning to his boyhood club for the first time, then inexplicably tried to backheel the ball to Wilshere on the edge the Arsenal penalty area, but gave it straight to Andres Iniesta.
Messi - who netted all four Barcelona goals in last season's game here - was away, and brilliantly chipped Almunia before lashing the ball into the empty net.
Arsenal looked to be facing an uphill battle for the second half, but were presented with a lifeline on 53 minutes.
Samir Nasri got away down the left and won a corner which he swung into the six-yard box where Busquets headed it past his own goalkeeper.
The tie then took another twist when van Persie latched onto a throughball, but was ruled offside, which looked marginal.
The Holland forward lashed the ball wide and was shown a second yellow card, swiftly followed by a red.
Van Persie and the Arsenal players could not believe it, as the striker claimed he could not hear the whistle.
Barcelona started the onslaught almost immediately, with first David Villa and then Messi denied by a couple of brave blocks from Almunia.
The Catalans finally regained the advantage on 68 minutes when Xavi slotted home after being played in following a quick exchange between Iniesta and Villa.
Before Arsenal could regroup, Barcelona were awarded a penalty when Koscielny tripped Pedro and Messi slotted it into the bottom corner to put Barcelona within touching distance of the last eight.
Wenger sent on Andrey Arshavin and then Nicklas Bendtner, replacing Fabregas, but it was more in hope than expectation.
Almunia denied Barcelona another goal with good blocks from Messi and substitute Ibrahim Afellay.
Bendtner was agonisingly close to connecting with Wilshere's cross into the six-yard box, but it was not to be for the Gunners.