Nicklas Bendtner had fired the Gunners into a shock lead on 18 minutes. However, Messi soon drew Barcelona level after capitalising on a mistake by Mikael Silvestre.
The Argentina forward then added a second from close range before dashing clear to make it 3-1 on the night just before the break, and grabbed a fourth with three minutes left to complete a comfortable 6-3 aggregate victory for the tournament holders.
Arsene Wenger's injury-hit squad - without the likes of captain Cesc Fabregas, Andrey Arshavin and Alex Song - must now regroup and focus on overhauling Chelsea and Manchester United in the Barclays Premier League title race.
Arsenal, playing in their white change kit, looked determined not to be overrun as they had during the opening exchanges of the first leg.
Barcelona, however, created an couple of chances when Xavi, captain for the night in the absence of suspended Carles Puyol, flicked the ball wide before Messi fired an angled shot just over the bar in a sign of things to come.
The English side, though, snatched a shock lead on their first real chance after 18 minutes.
Theo Walcott was put clear by Abou Diaby down the right, and he dashed into the Barca penalty area before squaring to Bendtner.
Victor Valdes made a good reaction save, but the in-form Denmark striker was quick to stab the rebound into the net and put the English team ahead in the tie for the first time.
The Gunners then wasted another chance of a breakaway, as Diaby pushed the ball left to Bendtner when Walcott was in space on the right.
It proved a costly error as Barcelona went up the other end to equalise on 21 minutes.
Silvestre, in the side ahead of veteran Sol Campbell who was not fully fit, failed to clear the ball on the edge of the Arsenal penalty area - and Messi needed no second invitation, lashing his shot into the top right corner.
Messi continued to torment Arsenal as he collected the ball on the right touchline before weaving into the box and drilling a shot into the side netting.
Arsenal were again punished by Messi for some poor defending as Barcelona went 2-1 ahead on 37 minutes.
Eric Abidal crossed the ball into the Arsenal box from the right, which was cut out by Thomas Vermaelen. However, his team-mates were slow to react as Pedro knocked the loose ball out to Messi - and he smashed it past Almunia.
The Argentina international completed a stunning hat-trick four minutes before the break when he latched onto a header from Abidal to race clear before dispatching a brilliant chip over the Arsenal keeper.
Messi nearly had another at the start of the second half when Pedro whipped a low ball across the Arsenal six-yard box from the right, which was just too far ahead of the Barcelona forward.
Arsenal had little choice but to go forwards, but that left the visitors exposed at the back.
The visitors nearly found away through when Diaby stabbed the ball to Bendtner just inside the Barcelona box, but the Denmark striker was hustle out of possession before he could shoot.
Then when left-back Gael Clichy broke and fed Bendtner, the home defence again got back in numbers to clear.
Diaby's low ball across the edge of the Barcelona box went all the way through to Tomas Rosicky, but the Czech snatched at his shot, which flew harmlessly wide.
Messi's clever quick free-kick released Pedro, but his angled chip was off target, before at the other end Bendtner's header crashed against the post - but the offside flag was up.
With 18 minutes left, Wenger sent on Eduardo for Rosicky, with Samir Nasri moving out to the left in a 4-4-2.
Clichy knocked Alves off the ball to charge forwards, but, with team-mates well placed, drilled an ambitious shot over from 20 yards.
Maxwell forced Almunia into a good save at his near post after cutting into the right side of the Arsenal penalty area.
Messi then completed a fine night's work with another well-taken goal three minutes from time as the holders marched on towards a mouth-watering semi-final clash against Jose Mourinho's Inter Milan.