Pierre-Emerick Aubameyang scored a hat-trick and Hector Bellerin added a fourth as the Gunners go in front of their visitors, who saw Pascal Struijk and Helder Costa find the back of the net.
The win lifts Arsenal to 10th place in the Premier League, two points and one place above Leeds, who lost for the second time in their last three outings.
Story of the match
Leeds had the first chance of the match on 12 minutes as Jack Harrison sent in a cross from the wing to Patrick Bamford, whose header was comfortably saved by Arsenal goalkeeper Bernd Leno.
A minute later, the Gunners were in front. Aubameyang cut in from the left and, following a step-over, fired low into the net that keeper Ilian Meslier could only get his fingertips on.
Jamie Shackleton, starting in place of Kalvin Phillips, chipped the ball in for Raphinha, who found Harrison, however, his shot was saved well by Leno.
Luke Ayling spared the visitors' blushes after making a goal-saving dive from Aubameyang's effort, which saw the ball pulled back for him by David Luiz.
Arsenal had been awarded a penalty after Liam Cooper had brought down Bukayo Saka, only to see it overturned by referee, Stuart Attwell.
Saka won the Gunners a second penalty, this one standing.
Aubameyang converted in the 41st minute to double the hosts' lead. Just before halftime, it was three, as Hector Bellerin smashed one past Meslier.
Inside of two minutes from the half time restart, Arsenal made it 4-0 as Emile Smith-Rowe chipped it into the six-yard box and found Aubameyang, who completed his hat-trick.
In the 58th minute, Leno tipped behind Raphinha's header and the Brazilian's corner was powered home by Pascal Struijk to reduce the deficit to 4-1.
Ten minutes later, the margin was halved, as Raphinha slipped in Tyler Roberts and he found Helder Costa, whose right-footed finish inside the box made it 4-2.
Bamford thought he had a penalty on 75 minutes, but his appeals were waved away while Aubameyang hit the woodwork, in what proved to be the last chance of the match, as Arsenal picked up three much-needed points.
Man of the match: Pierre-Emerick Aubameyang
His goal total now up to eight for the season, the Gabonese hitman carried his side to victory on the back of what may have been his finest performance in an Arsenal shirt, delivering three crucial points to the Gunners.
Arsenal played a brilliant game in attack
It was all there for the Gunners: pressing Leeds, moving into open space and passing with a real sense of vision. The front four of Smith-Rowe, Aubameyang, Saka and Martin Odegaard led the way - while Granit Xhaka and Dani Ceballos formed a solid foundation and even Bellerin was given license to attack from his right-back spot.
Leeds' defence continues to be a problem
As a newly-promoted side with a wide-open style, there were always going to be goals for both the Whites and their opponents, but they've given up 16 since the calendar turned to 2021.
Even with Diego Llorente and Kalvin Phillips out, this is not acceptable and something that Marcelo Bielsa will need to fix going forward if the Whites want to be more than just a mid-table team.