The Brazilian star headed past Jens Lehmann with only seven minutes of the last 16 clash remaining to ensure the second leg encounter at the Emirates Stadium ended 1-1 as Ronald Koeman's side won 2-1 on aggregate.
It was Arsenal's third cup exit in only ten days following their Carling Cup final defeat to Chelsea and the FA Cup loss at Blackburn Rovers.
Arsene Wenger's side dominated the match but, not for the first time this season, were made to pay for a host of missed chances.
After making a sluggish start, Arsenal created their first chance in the eighth minute when Kolo Toure did brilliantly to get to the byline only to then have a rush of blood to the head as he fired feebly wide when a cross was by far the better option.
In the 16th minute, after some concerted Gunners pressure, Cesc Fabregas found Emmanuel Adebayor inside the penalty area, but the Togo striker's first touch was poor and PSV keeper Gomes was able to smother his shot.
As Arsenal stepped up the pace, Toure's angled drive was parried by Gomes before Adebayor heads narrowly wide. A patient build-up then ended with Julio Baptista's spectacular volley going over the bar.
Adebayor, who had looked awkward on the ball at times, suddenly turned well inside the area but his shot was blocked by Alex.
In a rare PSV attack just after the half-hour mark, an unmarked Phillip Cocu flicked a header wide from Edison Mendez's cross.
As the first half drew to a close, a spectacular overhead kick by Baptista drifted wide of Gomes' goal while, at the other end, Jefferson Farfan profited from a Gilberto Silva mistake before falling over the Arsenal captain. The referee merely waved away the penalty appeals though.
Arsenal finally broke the deadlock in the 58th minute. Denilson whipped in a corner and, in the ensuing confusion, the ball deflected off the unfortunate Alex and dribbled into the net.
Almost immediately Adebayor had a great chance to make it 2-0 but blasted a fine strike straight at Gomes before Alex Hleb set up Fabregas only for the Spanish teenager's shot from just inside the area to curl inches over the bar.
PSV were denied what appeared to be a certain penalty when Denilson appeared to trip Farfan - but amazingly the referee saw no infringement.
Thierry Henry came on as a substitute midway through the second half and forced Gomes to make two saves but the Frenchman looked far from fit.
It was left to Alex to have the final say, leaping above Abou Diaby to plant an 83rd-minute header into the net.
There was still time for PSV to almost score again but Jason Culina lashed a shot into the side-netting. However, they had already done enough to progress to Friday's quarter-final draw after knocking out last season's beaten finalists.