Match Summary
The Red Devils' poor recent struggles persisted at Elland Road, but manager the Portuguese tactician had Matheus Cunha to thank for his side not suffering even more damage against Leeds.
Dominic Calvert-Lewin directed a first-half attempt against the woodwork for the in-form home team before Brenden Aaronson finished superbly with a driven, 62nd-minute effort.
With the goal, Amorim was under intense scrutiny after his side had been held by struggling Wolverhampton Wanderers at home earlier in the week.
Nevertheless, against opponents who had less time to prepare, Cunha restored parity three minutes later when he ran on to a through ball from substitute the Dutchman and guided a shot underneath advancing Leeds goalkeeper Lucas Perri.
It was only the Brazilian's fourth goal since his high-profile summer move and came at a time when the manager is without several key attacking players due to a combination of fitness issues and international duty.
Not that you would expect the hosts to care about that given their own lack of preparation time.
The Swiss attacker forced a full length save out of Manchester United goalkeeper Senne Lammens with a audacious overhead kick, and visiting heads were in hands when the Slovenian striker, who is struggling to make an impact, turned his teammate's cut-back wide from close range.
The goalscorer, who had a goal ruled out for offside much earlier in the match, also fired against a post late on.
The point extends the home side's unbeaten run to seven games, their best such streak since over two decades ago, and takes them a significant margin 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, squandered.
With the Africa Cup of Nations reaching its knockout phase, the United coach could be forgiven for hoping the participating nations make a pretty quick exit.
Existing injuries to skipper Bruno Fernandes and England international Mason Mount only exacerbated the impact the unavailability of other attackers is having on the team's squad.
It's not that the missing pair are the solution to all of United's problems. After all, they were part of the side that suffered poor results earlier in the campaign.
But without them, Amorim has limited attacking options.
He evidently does not trust youngster Shea Lacey or the seasoned Zirkzee, even though the Dutch forward provided the through ball for the equaliser almost instantly after his introduction as a replacement.
That leaves Cunha, who has now scored three goals in five games, and others playing out of their natural positions, alongside Benjamin Sesko.
On this evidence, the big-money frontman looks similar to previous underwhelming signings, lacking in confidence and assurance 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 memorable victories in their last few home games, the arrival of their fiercest rivals to Elland Road was a bit drab affair.
True, there were instances of typical fervor, but the intimidating edge was not as evident as in previous encounters.
Leeds' fans were more concerned about their side's inability to get sustained possession in dangerous areas for any length of time.
The Calvert-Lewin header that clipped the post was an rare moment of quality in a tight first half.
It still felt as though the hosts were finding it tough when a mistake opened the door for the opener.
Ever so briefly, Leeds' ecstatic fans thought they were about to secure a rare win against their old foes.
Nevertheless, there is a much bigger picture for the manager and Leeds to deal with.
When they endured a difficult run of form earlier in the season, many speculated about the manager's position.
In contrast, he is now overseeing clear progress.
The job is not completed yet but step by step, the team are getting closer to securing their survival.
The Yorkshire club have a Premier League trip to Newcastle in midweek, followed by the start of their domestic cup campaign next weekend. Manchester United face a league trip to Turf Moor before also entering their FA Cup journey with a Old Trafford tie.
Elara is a music journalist and cultural critic with a passion for uncovering emerging artists and trends across genres.