The Gunners were forced to raise their game after James Justin gave the visitors the lead with a powerful strike in the 55th minute. However, Arsenal responded through defender Ricardo Calafiori before Bruno Guimaraes struck the decisive goal to complete the comeback.
David Raya was one of Arsenal's busiest players in the first half, producing several important saves to keep the hosts in the contest as Leeds threatened to take control.
Arsenal created the first meaningful opportunity in the 21st minute when Kai Havertz found space inside the box, but his header drifted wide of the target.
Leeds gradually grew into the game, with Jayden Bogle capitalising on a loose ball to test Raya, who was equal to the effort.
Bukayo Saka and Noni Madueke attempted to combine in an effort to unlock Leeds' stubborn defence, but the visitors remained organised and disciplined at the back.
Raya was called into action again just after the half-hour mark, denying Ethan Ampadu as Leeds continued to threaten.
Arsenal responded with another promising move created by Madueke, but Havertz was unable to direct his header on target.
Before the interval, Raya produced another impressive save to keep out a thunderous effort from Gabriel Gudmundsson at the back post, ensuring the teams went into half-time level.
The second half brought greater intensity as both sides pushed for the breakthrough.
Leeds made a strong start after the restart and were rewarded in the 55th minute when Justin unleashed a powerful shot to put the visitors ahead.
Arsenal responded positively, with Calafiori restoring parity in the 62nd minute to give the home supporters renewed hope.
The Gunners continued to press for a winner, while Leeds refused to retreat into their shell and remained dangerous on the counterattack.
However, Arsenal eventually found the decisive breakthrough following a well-worked move involving Declan Rice, which ended with Guimaraes finding the top corner to seal a valuable victory for the London side.
Manchester United head coach Michael Carrick has urged everyone at the club, including the players and himself, to improve ahead of Sunday's Premier League clash against Bournemouth.
Joao Pedro has revealed how an early conversation with Cole Palmer helped build a friendship that has become central to Chelsea's attacking success.
Erling Haaland will be available for Manchester City's Premier League trip to Aston Villa on Saturday after recovering from the knock that ruled him out of their 5-1 Champions League victory over AEK Athens.
Bournemouth continued their perfect start to the Europa League league phase with a 3-0 victory over AC Milan, while Crystal Palace drew 2-2 with Besiktas in Istanbul and Juventus were held by Rennes by the same scoreline on Thursday.
