The Championship high-flyers squandered several golden opportunities in an impressive showing in north London, and were eventually made to pay for that after the interval.
Reiss Nelson’s second-half goal was enough to send the Gunners through, who will now travel to Bournemouth at the end of the month.
England Under-21 winger Nelson finished from close-range to settle a tie which saw the second tier leaders more than match their top-flight opponents for a large majority of the contest.
A decade on from a memorable FA Cup shock at rivals Manchester United, Leeds looked set to once again ruffle the feathers of the established order, only to fall agonisingly short after a fine display in front of a vast away following at the Emirates Stadium.
Arsenal head coach Mikel Arteta, taking charge of just his fourth match, must have displayed the half-time attributes of someone like his opposite number Marcelo Bielsa – whose first foray into management came when his counterpart was just eight years old – as Arsenal were a different prospect after a dismal first-half.
Leeds wasted a glut of chances to take the lead and make it a jittery night for Arteta and the home fans, Patrick Bamford coming closest when he rattled the frame of the goal.
But, after the break, Arsenal responded to whatever Arteta demanded of them and Nelson’s tap-in on 55 minutes was enough to seal a hard-fought victory.
Nicolas Pepe, having already enjoyed an early run at the Leeds defence, was the first to draw a save out of debutant Illan Meslier in the visitors’ goal.
But it was the second-tier side who were using the ball better in the opening stages, working it into dangerous positions without finding an end product.
They eventually tested Emiliano Martinez as Jack Harrison stung the palms of the stand-in Gunners goalkeeper, who was then helpless as Patrick Bamford’s strike cannoned back off the crossbar moments later.
Arsenal – as they have been so often this season – were creating their own problems as a number of misplaced passes out of defence from the likes of David Luiz and fit-again Rob Holding saw them caught out by a Leeds side full of pressing players.
Arteta’s surprise decision to deploy Sokratis Papastathopoulos at right-back was also looking questionable as the Greece international was easily beaten for pace by Ezgjan Alioski, who then angled a shot wide.
Despite all of Leeds’ attacking play, they should have been behind on the half-hour mark but Luiz could only head Mesut Ozil’s corner wide having been picked out free in the box.
At the other end, Martinez had to spring across his goal to keep out Alioski’s close-range header after the winger once again got the better of Sokratis.
Yet another opportunity went begging for the away side as Robbie Gotts, another man making his Leeds debut, miscued a strike as the Arsenal fans began to grow restless.
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