Key Moments
The Red Devils' disappointing recent struggles continued at Leeds' fortress, but head coach the Portuguese tactician had Matheus Cunha to thank for the team not suffering even more disappointment against their old rivals.
Dominic Calvert-Lewin directed a first-period effort against the woodwork for the in-form home team before Brenden Aaronson finished superbly with a low, 62nd-minute shot.
At that stage, the United boss was under intense scrutiny after his side had failed to beat bottom-of-the-table Wolverhampton Wanderers at Old Trafford earlier in the week.
Nevertheless, against a team who had two days less to recover, Cunha levelled three minutes after the opener when he latched onto a through ball from substitute Joshua Zirkzee and slid a shot underneath rushing Leeds goalkeeper Lucas Perri.
It was only the Brazilian's fourth Premier League goal since his big-money 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.
Noah Okafor forced a diving 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 finding it hard to make an impact, turned Zirkzee's cut-back wide from six yards out.
Cunha, who had a goal disallowed for offside much earlier in the match, also blasted against a post late on.
The draw extends Leeds' unbeaten run to seven games, their longest such streak since 2001, 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 matter of hours, wasted.
With the Africa Cup of Nations reaching its latter stages, the United coach could be forgiven for hoping the involved countries make a pretty quick exit.
Current injuries to skipper Bruno Fernandes and Three Lions star Mason Mount only exacerbated the impact the absence of other attackers is having on the team's squad.
It's not that the missing pair are the solution to all of the club's problems. After all, they were part of the side that experienced disappointing results earlier in the campaign.
But without them, the boss has few attacking options.
He evidently does not have full faith in youngster Shea Lacey or the much more experienced Zirkzee, even though the Netherlands forward delivered the assist for the equaliser almost instantly after his introduction as a substitute.
That leaves Cunha, who has now scored three goals in recent outings, and others operating out of their preferred positions, alongside Benjamin Sesko.
On this evidence, the big-money frontman looks no better than previous underwhelming signings, lacking in belief and conviction in front of goal.
Sesko's failure to turn home the cross means it is now a long run without a goal for the new signing.
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 moments of typical fervor, but the intimidating edge was not as pronounced as in previous fixtures.
Leeds' fans were more concerned about their side's struggle to get worthwhile possession in dangerous areas for any length of time.
The Calvert-Lewin header that clipped the post was an rare moment of threat in a tight first half.
It still felt as though Leeds were finding it tough when a defensive error opened the door for Aaronson.
Ever so briefly, Leeds' ecstatic fans thought they were about to secure a rare win against Manchester United.
However, there is a much bigger picture for the manager and the club to deal with.
When they suffered a poor run of form earlier in the season, many thought about the manager's position.
In contrast, he is now masterminding clear progress.
The job is not completed yet but step by step, the team are getting nearer to achieving their survival.
The Yorkshire club have a top-flight trip to Newcastle in midweek, followed by the start of their domestic cup campaign next weekend. The Red Devils face a Premier League trip to Burnley before also beginning their FA Cup journey with a home tie.
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