The Whites were the better side throughout at Elland Road, but despite Nicolas Pepe’s second half red card, Bielsa’s couldn’t force the win.
Leeds had the better of a tight first half, as Raphinha and Mateusz Klich both fired wide and Bernd Leno produced a instinctive stop to deny Patrick Bamford before the break.
The hosts lack of killer instinct meant Arsenal stayed in the game after the restart, but Mikel Arteta’s side shot themselves in the foot on 50 minutes.
Pepe clashed off the ball with Ezgjan Alioski, and after a quick VAR check, Anthony Taylor sent him off for a clear headbutt.
With a man advantage in the final half hour, Leeds did push for a winner, but Leno proved to be a vital barrier for Arteta.
The German produced a huge stop to deny Stuart Dallas on 66 minutes before blocking another effort from substitute Rodrigo.
But as the game began to see saw in the final ten minutes, both sides had chances to win it.
Rodrigo and Bamford were both denied by the woodwork before the anonymous Illan Meslier to deny Bukayo Saka.
But despite the late flurry of chances, this game was destined to stay goalless.
Full Time at Elland Road it’s Leeds United 0 Arsenal 0