Match Summary
The Red Devils' disappointing recent struggles continued at Leeds' fortress, but head coach the Portuguese tactician had Matheus Cunha to thank for his side avoiding even more damage against Leeds.
Dominic Calvert-Lewin headed a first-half effort against the post for the confident home team before the American midfielder applied a cool finish with a low, 62nd-minute shot.
At that stage, Amorim was under intense scrutiny after his side had been held by struggling Wolves at home earlier in the week.
Nevertheless, against opponents who had two days less to recover, the forward restored parity three minutes after the opener when he latched onto a pass from introduced Joshua Zirkzee and guided a finish 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 the manager is without several key attacking players due to a mix 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 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 struggling to make an impact, turned his teammate's cut-back wide from six yards out.
Cunha, who had a goal ruled out for offside much earlier in the contest, also fired against a post late on.
The draw extends the home side's unbeaten run to seven matches, their longest such streak since over two decades ago, and takes them a significant margin clear of the relegation zone.
For the Manchester United though, it was yet another chance to move into fourth spot, albeit only for a matter of hours, wasted.
With the Africa Cup of Nations reaching its latter stages, the United coach could be understood for hoping the participating nations make a pretty quick exit.
Existing injuries to captain Bruno Fernandes and England international Mason Mount only heightened the impact the unavailability of other attackers is having on Amorim's options.
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 poor results earlier in the season.
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 Joshua Zirkzee, even though the Dutch forward provided the assist for Cunha's equaliser almost instantly after his arrival as a substitute.
That leaves Cunha, who has now scored three goals in recent outings, and others operating out of their natural positions, alongside Benjamin Sesko.
On this showing, the big-money frontman looks no better than previous underwhelming signings, lacking in confidence and assurance in front of goal.
Sesko's failure to turn home the cross means it is now a long run without a goal for the young striker.
After memorable 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 expected fervor, but the intimidating edge was not as evident as in other fixtures.
The home fans were more concerned about their side's inability to get worthwhile possession in advanced areas for any length of time.
The Calvert-Lewin header that struck the post was an rare moment of threat in a congested first half.
It still felt as though Leeds were finding it tough when a defensive error opened the door for the opener.
For a short moment, Leeds' delirious fans thought they were about to secure a coveted win against their old foes.
Nevertheless, 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 season, many speculated about the manager's position.
In contrast, he is now overseeing clear improvement.
The job is not done yet but gradually, the team are getting nearer to achieving their survival.
The Yorkshire club have a top-flight trip to St James' Park in midweek, followed by the start of their FA Cup campaign next weekend. Manchester United face a Premier League trip to Turf Moor before also entering their FA Cup journey with a Old Trafford tie.
Lena is a digital strategist and founder passionate about crafting unique brand identities and user-centered designs.