Eddie Nketiah has scored nine goals in all competitions this season
It was a fourth successive win for Mikel Arteta's side and one that puts them firmly in the driving seat for a top-four spot before Thursday's north London derby at Tottenham.
But Leeds' early capitulation was entirely of their own making, with goalkeeper Illan Meslier gifting the hosts an opener before captain Luke Ayling was sent off for a needless lunge on Gabriel Martinelli.
Eddie Nketiah pounced on Meslier's loose touch to open the scoring and then finished a swift move to double the Gunners' lead before Ayling's rash challenge left Leeds a man down for more than an hour.
The Elland Road outfit did not have an effort on goal until Diego Llorente headed past Aaron Ramsdale in the 66th minute to tee up more of a nervy finish than anyone inside Emirates Stadium would have anticipated.
Leeds applied some late pressure, sending Meslier up for set-pieces, but the fourth-placed hosts were never seriously in danger of losing their lead and now hold a four-point lead over Tottenham in fifth.
Defeat for Leeds, coupled with Everton's win at Leicester, means Jesse Marsch's side slip into the bottom three with three games remaining.
Eddie Nketiah played 19 times on loan for Leeds in the 2019-20 season
With Spurs drawing at Liverpool on Saturday, Arsenal knew if they could successfully navigate this potential stumbling block they would head into one of the most crucial north London derbies in recent years on Thursday with a commanding lead over their rivals.
The hosts were handed the ideal start when Meslier took a loose touch from Ayling's pass and allowed Nketiah to pounce for the opener - a reward for both his persistent pressing and recent performances leading the Arsenal line.
The 22-year-old's forward's future is yet to be determined, with his contract expiring in the summer, but Nketiah has continued to do his bit to make sure Arsenal are playing in Europe's elite competition next term, and doubled the hosts' lead with a well-taken second from Martinelli's pass in the 10th minute.
That was the forward's ninth goal this season, although five of those have come in the Carabao Cup, where he was used most frequently before earning a first Premier League start of the season last month and establishing his place in Arteta's first XI.
Now the soon-to-be-free-agent is spearheading a young and exciting Arsenal forward line alongside Bukayo Saka and Martinelli, who was on the end of a foolish tackle from Ayling that resulted in the defender being dismissed after 27 minutes.
Arsenal's flowing attack toyed with the visitors as Martin Odegaard's free-kick found its way onto the bar and Martinelli poked a half-volley over, only for the Gunners to be caught out from Leeds' first corner.
It made things slightly less comfortable than Arteta will have hoped for but his side got the vital win they needed before a trip to Tottenham Hotspur Stadium, where victory will confirm Arsenal's return to the Champions League for the first time since 2016-17.
On top of Ayling's sending off, Leeds received two yellow cards to take them to 96 this season - more than any side in Premier League history
Leeds looked to have turned a corner under new boss Marsch, collecting three wins in a five-game unbeaten run before being humbled 4-0 by league leaders Manchester City last time out.
That might have been enough to drag them to safety were it not for recent revivals from Burnley and Everton, but Marsch's side now find themselves on the brink of a return to the Championship.
The American must have watched on in disbelief as Meslier took a poor touch in his six-yard box to allow former Leeds loanee Nketiah to open the scoring after five minutes.
He will have been even more dumbfounded by captain Ayling, on his 500th career appearance, diving in on Martinelli when the visitors were trailing 2-0.
The defender was initially shown a yellow card, but VAR recommended referee Chris Kavanagh look at the pitch-side monitor and he upgraded it to red.
Raphinha almost followed the Leeds skipper for his reaction and the visitors threatened to unravel as home fans taunted them with chants of "you're going down".
Despite their numerical disadvantage, Leeds rediscovered some defensive solidity and made their first opportunity at the other end count when Junior Firpo flicked on a corner for Llorente to score.
Rodrigo had a chance to snatch a draw in stoppage time but could not get enough on his header, leaving Leeds 18th, level on points with Burnley and one behind Everton but with a far worse goal difference, as they finish the day in the bottom three for the first time since October.
-- Courtesy of BBC Sport