Neither side were able to break the other down for the majority of the match, but a late handball from Marc Guehi gave the hosts the chance to secure the win.
After a VAR review, the Brazilian stepped up and sent Eagles goalkeeper Vicente Guita the wrong way.
At 0-0 though, Christian Benteke missed a glorious chance to give the Eagles the lead but just a few yards out he could only place his header wide.
In typical fashion, one of their more dangerous players, Wilfried Zaha was heavily involved in the chance after he stood the ball up for the Belgian who will undoubtedly be losing sleep over that miss.
Even after missing that chance, the former Liverpool striker still could have won the game after getting a toe on the end of a Jordan Ayew cross and just as the ball looked like it was creeping in, Leeds goalkeeper Illan Meslier reacted in time to stop the ball from crossing over the line.
It's now back-to-back defeats for Patrick Vieira after they lost to Steven Gerrard's Aston Villa in their last match.
Whilst the Arsenal legend would have been disappointed in coming away with nothing from the match, on another day, Benteke would have converted those chances and his side would have come away with the victory.
More alarmingly though is the Eagles' habit of conceding late goals.
Against Leeds, it was the third time this season that Viera's side have conceded a goal after 90 minutes had been played.
The other occasions were against the Gunners when Alexandre Lacazette netted in the 95th minute and against Brighton where Neal Maupay also converted at the same time from the spot.
Things are still very much on the up for the Eagles though who have been playing some excellent football at times this season.
They will desperately be hoping to get back on track when they travel to Old Trafford to face Manchester United.
Meanwhile Bielsa will hope that this win is a springboard for a another when they take on Brentford at Elland Road.