At a Glance
The Red Devils' poor run of form continued at Leeds' fortress, but manager the Portuguese tactician had his Brazilian forward to thank for the team avoiding even more damage against their old rivals.
Dominic Calvert-Lewin headed a first-period effort against the woodwork for the confident home team before Brenden Aaronson finished superbly with a driven, 62nd-minute effort.
At that stage, the United boss was under intense scrutiny after his side had been held by struggling Wolverhampton Wanderers at home earlier in the week.
However, against a team who had two days less to prepare, Cunha levelled three minutes later when he ran on to a pass from introduced Joshua Zirkzee and guided a shot underneath rushing Leeds 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 combination of fitness issues and national team commitments.
Not that you would expect the hosts to sympathise with that given their own lack of preparation time.
The Swiss attacker forced a diving save out of Manchester United goalkeeper Senne Lammens with a audacious overhead kick, and visiting heads were in hands when Benjamin Sesko, who is struggling to make an impact, turned his teammate's cut-back wide from six yards out.
The goalscorer, who had a goal ruled out for offside much earlier in the contest, also fired against a post late on.
The point prolongs Leeds' unbeaten run to seven matches, their best such streak since 2001, and takes them a significant margin clear of the drop zone.
For the Manchester United though, it was yet another chance to move into the Champions League places, albeit only for a short time, squandered.
With the Africa Cup of Nations reaching its knockout phase, Amorim could be forgiven for hoping the involved countries make a swift exit.
Current injuries to skipper Bruno Fernandes and Three Lions star Mason Mount only exacerbated the impact the absence of other forwards is having on the team's options.
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 poor results earlier in the season.
But without them, the boss has limited alternatives in attack.
He evidently does not trust teenager Shea Lacey or the much more experienced Zirkzee, even though the Netherlands forward delivered the assist for Cunha's equaliser almost instantly after his introduction as a substitute.
That leaves the Brazilian, who has now scored a small tally in five games, and others operating out of their preferred positions, alongside Benjamin Sesko.
On this showing, the big-money frontman looks similar to previous struggling signings, lacking in belief and assurance in front of goal.
His failure to turn home Zirkzee's cross means it is now a long run without a goal for the young striker.
After thrilling victories in their last few home games, the arrival of their biggest rivals to Elland Road was a comparatively subdued affair.
True, there were instances of expected fervor, but the intimidating edge was not as evident as in other encounters.
The home fans were more preoccupied about their side's inability to get worthwhile possession in advanced areas for any prolonged period.
The Calvert-Lewin header that struck the post was an isolated moment of quality in a congested first half.
It still felt as though Leeds were struggling when a mistake opened the door for Aaronson.
For a short moment, The home ecstatic fans thought they were about to secure a rare win against Manchester United.
However, there is a wider context for the manager and Leeds 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 masterminding significant progress.
The task is not completed yet but step by step, Leeds 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 Premier League trip to Turf Moor before also entering their cup journey with a home tie.