Key Moments
The Red Devils' disappointing recent struggles persisted at Leeds' fortress, but head coach the Portuguese tactician had Matheus Cunha to thank for the team avoiding even more damage against their old rivals.
Dominic Calvert-Lewin headed a first-period effort against the post for the confident hosts before Brenden Aaronson applied a cool finish with a low, 62nd-minute shot.
With the goal, Amorim was in the firing line after his side had been held by bottom-of-the-table Wolves at Old Trafford earlier in the week.
However, against a team who had less time to prepare, Cunha restored parity three minutes after the opener when he ran on to a pass from introduced Joshua Zirkzee and slid a shot underneath advancing home 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 several key attacking players due to a combination of injury and national team commitments.
Not that you would expect Leeds to care about that given their own tight schedule.
The Swiss attacker forced a full length save out of visiting goalkeeper Senne Lammens with a spectacular overhead kick, and United heads were in hands when the Slovenian striker, who is finding it hard to make an impression, turned Zirkzee's cut-back wide from close range.
The goalscorer, who had a goal disallowed for offside much earlier in the match, also blasted against a post in the dying moments.
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 relegation zone.
For the visitors though, it was yet another chance to move into the Champions League places, albeit only for a short time, wasted.
With the Africa Cup of Nations reaching its latter stages, Amorim could be understood for hoping the participating nations make a swift exit.
Existing injuries to skipper Bruno Fernandes and Three Lions star Mason Mount only heightened the impact the absence of other forwards is having on the team's squad.
It's not that the absent players are the solution to all of the club'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 evidently does not trust youngster Shea Lacey or the seasoned Zirkzee, even though the Dutch forward delivered the assist for Cunha's equaliser almost immediately after his arrival as a replacement.
That leaves Cunha, who has now scored three goals in five games, and others operating out of their preferred positions, alongside Benjamin Sesko.
On this showing, the expensive frontman looks no better than previous struggling signings, lacking in belief and conviction in front of goal.
His failure to turn home the cross means it is now a long run without a goal for the young striker.
After thrilling victories in their last few home games, the arrival of their biggest rivals to Elland Road was a bit drab affair.
True, there were instances of expected fervor, but the intimidating edge was not as pronounced as in other fixtures.
Leeds' fans were more concerned about their side's struggle to get worthwhile possession in advanced areas for any length of time.
The striker's header that struck the post was an isolated 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, The home delirious fans thought they were about to secure a coveted win against their old foes.
However, there is a much bigger picture for the manager and Leeds to deal with.
When they suffered a difficult run of form earlier in the campaign, many thought about the manager's position.
Instead, he is now overseeing clear improvement.
The job is not done yet but step by step, Leeds are getting nearer to securing their top-flight status.
The Yorkshire club have a Premier League trip to St James' Park in midweek, followed by the start of their domestic cup campaign next weekend. Manchester United face a Premier League trip to Burnley before also beginning their cup journey with a Old Trafford tie.
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