Key Moments
The Red Devils' disappointing run of form persisted at Leeds' fortress, but manager the Portuguese tactician had Matheus Cunha to thank for his side not suffering even more damage against their old rivals.
Dominic Calvert-Lewin headed a first-period attempt against the post for the confident hosts before the American midfielder finished superbly with a low, 62nd-minute effort.
With the goal, the United boss was under intense scrutiny after his side had been held by struggling Wolves at Old Trafford earlier in the week.
Nevertheless, against a team who had less time to recover, the forward restored parity three minutes later when he latched onto a through ball from substitute the Dutchman and guided a finish 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 Amorim is without four key attacking players due to a mix of fitness issues and national team commitments.
Not that the hosts to sympathise with that given their own tight schedule.
Noah Okafor forced a full length save out of Manchester United goalkeeper Senne Lammens with a spectacular 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 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 extends the home side's unbeaten run to seven matches, their best such streak since over two decades ago, and takes them a significant margin clear of the drop zone.
For the visitors 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, Amorim could be understood for hoping the participating nations make a pretty quick exit.
Existing injuries to skipper Bruno Fernandes and Three Lions star Mason Mount only heightened the impact the unavailability of other forwards is having on Amorim'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 experienced poor results earlier in the campaign.
But without them, the boss has few alternatives in attack.
He clearly does not have full faith in teenager Shea Lacey or the much more experienced Zirkzee, even though the Netherlands forward provided the assist for Cunha's equaliser almost immediately after his introduction as a replacement.
That leaves Cunha, who has now scored three goals in recent outings, and others playing out of their natural positions, alongside Benjamin Sesko.
On this showing, the big-money frontman looks similar to previous underwhelming signings, lacking in belief 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 thrilling victories in their previous home games, the arrival of their fiercest rivals to Elland Road was a comparatively subdued affair.
True, there were instances of expected fervor, but the intimidating edge was not as evident as in previous encounters.
The home fans were more concerned about their side's struggle to get sustained possession in advanced areas for any length of time.
The striker's header that clipped the post was an isolated moment of threat in a tight first half.
It still felt as though Leeds were finding it tough when a mistake opened the door for the opener.
For a short moment, The home ecstatic fans thought they were about to secure a coveted win against their old foes.
However, there is a wider context for Daniel Farke and the club to deal with.
When they endured a difficult run of form earlier in the campaign, many thought about the manager's future.
In contrast, he is now overseeing clear improvement.
The task is not done yet but step by step, Leeds are getting nearer to achieving their survival.
Leeds have a Premier League trip to Newcastle 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 cup journey with a Old Trafford tie.
Elena Vance is a seasoned journalist and tech enthusiast, known for her insightful analysis and engaging storytelling across various media platforms.