Key Moments
The Red Devils' poor run of form persisted at Elland Road, but manager the Portuguese tactician had his Brazilian forward to thank for the team avoiding even more disappointment against their old rivals.
Dominic Calvert-Lewin headed a first-half attempt against the woodwork for the in-form hosts before the American midfielder finished superbly with a low, 62nd-minute effort.
At that stage, the United boss was in the firing line after his side had been held by bottom-of-the-table Wolves at home earlier in the week.
However, against a team who had less time to recover, Cunha levelled three minutes after the opener when he ran on to a pass from introduced the Dutchman and slid a shot underneath rushing home goalkeeper Lucas Perri.
It was only the South American's fourth goal since his high-profile summer move and came at a time when the manager is without several key attacking players due to a mix of fitness issues and national team commitments.
Not that you would expect the hosts to care about that given their own lack of preparation time.
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 Benjamin Sesko, who is struggling to make an impression, turned Zirkzee's cut-back wide from close range.
The goalscorer, who had a goal ruled out for offside much earlier in the contest, also fired against a post late on.
The draw prolongs the home side's unbeaten run to seven games, their longest such streak since 2001, and takes them eight points clear of the relegation zone.
For the visitors 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, Amorim could be understood for hoping the involved countries 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 attackers is having on Amorim'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 disappointing results earlier in the campaign.
But without them, the boss has few attacking options.
He evidently does not trust youngster Shea Lacey or the much more experienced Joshua Zirkzee, even though the Dutch forward provided the through ball for Cunha's equaliser almost instantly after his arrival as a replacement.
That leaves the Brazilian, who has now scored three goals in five games, and others operating out of their natural positions, alongside Sesko.
On this evidence, the big-money frontman looks no better than previous struggling signings, lacking in confidence and conviction in front of goal.
His failure to turn home Zirkzee's cross means it is now nine games without a goal for the new signing.
After thrilling victories in their last few home games, the arrival of their fiercest rivals to Elland Road was a comparatively subdued affair.
True, there were instances of typical fervor, but the intimidating edge was not as evident as in previous fixtures.
The home fans were more concerned about their side's struggle to get worthwhile possession in dangerous areas for any prolonged period.
The striker's header that clipped the post was an isolated moment of quality in a tight first half.
It still felt as though Leeds were finding it tough when a mistake opened the door for the opener.
Ever so briefly, The home ecstatic fans thought they were about to secure a rare win against their old foes.
Nevertheless, there is a much bigger picture for the manager and the club to deal with.
When they endured a difficult run of form earlier in the season, many thought about the manager's future.
In contrast, he is now overseeing clear progress.
The task is not completed yet but step by step, the team are getting nearer to achieving their survival.
Leeds have a Premier League trip to St James' Park in midweek, followed by the start of their FA Cup campaign next weekend. Manchester United face a league trip to Turf Moor before also beginning their FA Cup journey with a home tie.
A tech journalist with over a decade of experience covering AI, cybersecurity, and consumer electronics across Europe.