Further goals from Nicklas Bendtner and Robin van Persie ensured that the Gunners will play host to Burnley in round five.
The return of Eduardo to the Arsenal first-team almost a year to the day since breaking his leg heightened the expectancy for an already electric FA Cup atmosphere.
Arsenal looked much sharper from the opening whistle and should have been three goals up within the first seven minutes.
The first opportunity feel to Nicklas Bendtner on four minutes after Bacary Sagna sent over a cross on to the head of the young Dane, but the Gunners striker headed the ball fractionally wide with the keeper well beaten.
Within seconds Carlos Vela accelerated through the middle before despatching a fierce drive that Tom Heaton could not hold. The Cardiff goalkeeper parried the ball into the path of Bendtner, whose shot he saved.
Heaton was again on hand to deny the Gunners after seven minutes with a point-blank save from William Gallas, whose shot from an acute angle was blocked by the Cardiff keeper.
Eduardo was looking sharp and dangerous and with 20 minutes on the clock, Vela got to the by-line on the left side of the area before crossing into the area, where the Croatian striker headed the ball home to spark a glorious celebration.
The Gunners doubled their lead on 35 minutes through Bendtner, who rose highest to head home Samir Nasri's cross from the left.
A combination of Heaton and the post prevented the Gunners from going 3-0 up on the stroke of half-time. The Bluebirds keeper first blocked Vela's shot, then the rebound fell to Bendtner, who hit the post.
When the ball bounced back to the Dane his effort was goalbound, but Heaton was on hand to make another timely block.
Arsenal were awarded a penalty on the hour after Gavin Rae hauled down Eduardo. The Croatian stepped up to take the kick himself, sending Heaton the wrong way to make it 3-0 before running to hug Arsenal fitness coach Tony Colbert, who has been instrumental in the striker's comeback.
Substitutes van Persie and Amaury Bischoff both went close with shots from acute angles on the left edge of the area, but again Heaton was on top form.
There was little he could do however in the 89th minute when van Persie raced on to a through-ball from Bendtner before firing right-footed into the left corner of the net.
A fifth goal should have followed a minute later, but van Persie was denied by the left upright and referee Mark Halsey brought the game to an end seconds later.