Match Summary
The Red Devils' disappointing run of form continued at Elland Road, but manager the Portuguese tactician had Matheus Cunha to thank for his side avoiding even more disappointment against their old rivals.
Dominic Calvert-Lewin headed a first-half effort against the woodwork for the in-form hosts before Brenden Aaronson 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 bottom-of-the-table Wolverhampton Wanderers at Old Trafford earlier in the week.
However, against opponents who had less time to prepare, Cunha restored parity three minutes after the opener when he ran on to a through ball from introduced the Dutchman and slid a shot underneath advancing Leeds goalkeeper Lucas Perri.
It was only the Brazilian's fourth Premier League goal since his high-profile summer move and came at a time when Amorim is without four key attacking players due to a combination of fitness issues and international duty.
Not that Leeds to sympathise with that given their own tight schedule.
Noah Okafor forced a diving 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 finding it hard to make an impression, turned Zirkzee's cut-back wide from close range.
Cunha, who had a goal disallowed for offside much earlier in the match, 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 eight points clear of the drop zone.
For the Manchester United though, it was yet another opportunity to move into fourth spot, albeit only for a short time, wasted.
With the AFCON reaching its latter stages, Amorim could be understood for hoping the involved countries make a pretty quick exit.
Current injuries to captain Bruno Fernandes and England international Mason Mount only heightened the impact the unavailability of other forwards is having on the team's options.
It's not that the absent players are the answer 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 clearly does not have full faith in youngster Shea Lacey or the seasoned Zirkzee, even though the Netherlands forward provided the assist for the equaliser almost instantly after his arrival as a substitute.
That leaves the Brazilian, who has now scored three goals in five games, and others playing out of their natural positions, alongside Benjamin Sesko.
On this showing, the expensive frontman looks similar to previous struggling signings, lacking in belief 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 new signing.
After memorable victories in their last few home games, the arrival of their biggest rivals to home was a comparatively subdued affair.
True, there were instances of expected fervor, but the intimidating edge was not as evident as in other encounters.
Leeds' fans were more concerned about their side's struggle to get worthwhile possession in advanced areas for any length of time.
The Calvert-Lewin header that clipped the post was an rare moment of threat in a congested first half.
It still felt as though the hosts were finding it tough when a defensive error opened the door for Aaronson.
For a short moment, Leeds' delirious fans thought they were about to secure a coveted win against their old foes.
Nevertheless, there is a wider context for the manager and the club to deal with.
When they suffered a difficult run of form earlier in the season, many thought about the manager's future.
Instead, he is now masterminding significant improvement.
The job is not completed yet but gradually, the team are getting closer to achieving their top-flight status.
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. The Red Devils face a Premier League trip to Turf Moor before also beginning their FA Cup journey with a home tie.
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