At a Glance
Manchester United's poor recent struggles persisted at Leeds' fortress, but manager the Portuguese tactician had his Brazilian forward 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 finished superbly with a driven, 62nd-minute shot.
With the goal, the United boss was under intense scrutiny after his side had failed to beat bottom-of-the-table Wolves at Old Trafford earlier in the week.
Nevertheless, against opponents who had less time to recover, Cunha levelled three minutes after the opener when he ran on to a through ball from substitute Joshua Zirkzee and guided a finish underneath advancing 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 Amorim is without several key attacking players due to a combination of injury and national team commitments.
Not that Leeds to sympathise with that given their own tight schedule.
The Swiss attacker forced a full length save out of Manchester United goalkeeper Senne Lammens with a spectacular overhead kick, and visiting heads were in hands when Benjamin Sesko, who is finding it hard 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 blasted against a post in the dying moments.
The draw prolongs Leeds' unbeaten run to seven matches, their best such streak since 2001, and takes them a significant margin clear of the relegation zone.
For the visitors though, it was yet another opportunity to move into fourth spot, albeit only for a short time, squandered.
With the Africa Cup of Nations reaching its latter stages, Amorim could be forgiven for hoping the involved countries make a swift exit.
Current injuries to captain Bruno Fernandes and England international Mason Mount only exacerbated the impact the unavailability of other forwards is having on the team's squad.
It's not that the absent players are the answer 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 attacking options.
He evidently does not have full faith in teenager Shea Lacey or the seasoned Zirkzee, even though the Netherlands forward provided the assist for the equaliser almost instantly after his arrival as a replacement.
That leaves the Brazilian, who has now scored a small tally in five games, and others playing out of their natural positions, alongside Benjamin Sesko.
On this showing, the expensive frontman looks similar to previous underwhelming signings, lacking in belief and conviction in front of goal.
Sesko's failure to turn home Zirkzee's cross means it is now nine games without a goal for the new signing.
After memorable victories in their previous home games, the arrival of their fiercest rivals to home was a comparatively subdued affair.
True, there were instances of expected atmosphere, but the hostile edge was not as pronounced as in previous fixtures.
The home fans were more concerned about their side's inability to get sustained possession in advanced areas for any length of time.
The Calvert-Lewin header that clipped the post was an rare moment of quality in a tight first half.
It still felt as though the hosts 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 Manchester United.
Nevertheless, there is a wider context 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 position.
In contrast, he is now overseeing clear improvement.
The task is not done yet but gradually, the team are getting closer to achieving their top-flight status.
The Yorkshire club have a Premier League trip to St James' Park in midweek, followed by the start of their FA Cup campaign next weekend. The Red Devils face a league trip to Turf Moor before also beginning their cup journey with a Old Trafford tie.