Match Summary
The Red Devils' poor run of form persisted at Elland Road, but manager the Portuguese tactician had Matheus Cunha to thank for the team not suffering even more damage against their old rivals.
Dominic Calvert-Lewin headed a first-period effort against the post for the confident home team before Brenden Aaronson applied a cool finish with a driven, 62nd-minute shot.
At that stage, the United boss was under intense scrutiny after his side had failed to beat struggling Wolves at Old Trafford earlier in the week.
However, against a team who had less time to recover, Cunha levelled three minutes later when he ran on to a pass from substitute Joshua Zirkzee and guided a shot underneath advancing home goalkeeper Lucas Perri.
It was only the South American's fourth goal since his big-money summer move and came at a time when the manager is without several key attacking players due to a mix of fitness issues and national team commitments.
Not that you would expect Leeds to sympathise with that given their own tight schedule.
Noah Okafor forced a diving save out of visiting goalkeeper Senne Lammens with a spectacular overhead kick, and visiting heads were in hands when Benjamin Sesko, who is finding it hard to make an impact, turned his teammate's cut-back wide from six yards out.
Cunha, who had a goal disallowed for offside much earlier in the match, also fired against a post in the dying moments.
The point prolongs the home side's unbeaten run to seven matches, their longest such streak since 2001, and takes them eight points clear of the drop zone.
For the Manchester United though, it was yet another opportunity to move into the Champions League places, albeit only for a short time, wasted.
With the AFCON reaching its latter stages, Amorim could be understood for hoping the involved countries make a pretty quick exit.
Existing injuries to captain Bruno Fernandes and England international Mason Mount only exacerbated the impact the unavailability of other attackers is having on Amorim's options.
It's not that the missing pair are the answer to all of United's problems. After all, they were part of the side that experienced disappointing results earlier in the campaign.
But without them, Amorim has few alternatives in attack.
He clearly does not trust youngster Shea Lacey or the much more experienced Joshua Zirkzee, even though the Dutch forward delivered the assist for Cunha's equaliser almost immediately after his introduction as a substitute.
That leaves Cunha, who has now scored a small tally in recent outings, and others operating out of their natural positions, alongside Sesko.
On this showing, the big-money frontman looks similar to previous struggling signings, lacking in confidence and conviction in front of goal.
His failure to turn home the cross means it is now nine games without a goal for the young striker.
After thrilling victories in their previous home games, the arrival of their fiercest rivals to home was a bit drab affair.
True, there were moments of typical atmosphere, but the intimidating edge was not as pronounced as in previous encounters.
The home fans were more concerned about their side's inability to get worthwhile possession in dangerous areas for any length of time.
The striker's header that clipped the post was an rare moment of quality in a congested first half.
It still felt as though the hosts were struggling when a mistake opened the door for Aaronson.
Ever so briefly, Leeds' delirious fans thought they were about to secure a coveted win against Manchester United.
However, there is a much bigger picture for the manager and Leeds to deal with.
When they endured a poor run of form earlier in the season, many thought about the manager's future.
Instead, he is now masterminding significant improvement.
The task is not done yet but gradually, the team are getting nearer to achieving their top-flight status.
The Yorkshire club have a top-flight trip to St James' Park in midweek, followed by the start of their domestic cup campaign next weekend. The Red Devils face a league trip to Burnley before also beginning their FA Cup journey with a home tie.
Elena is a certified nutritionist with 10 years of experience in sports supplementation and wellness coaching.