Key Moments
The Red Devils' poor recent struggles continued at Elland Road, but manager the Portuguese tactician had his Brazilian forward to thank for his side avoiding even more disappointment against Leeds.
The Everton loanee headed a first-half effort against the post for the in-form hosts before the American midfielder applied a cool finish with a low, 62nd-minute shot.
With the goal, Amorim 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 opponents who had two days less to prepare, Cunha restored parity three minutes later when he ran on to a pass from introduced the Dutchman and slid a shot 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 the manager is without several key attacking players due to a mix of fitness issues and international duty.
Not that you would expect the hosts to care about that given their own tight schedule.
Noah Okafor 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 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 extends the home side's unbeaten run to seven games, their best such streak since 2001, and takes them eight points clear of the drop zone.
For the visitors though, it was yet another opportunity to move into the Champions League places, albeit only for a short time, squandered.
With the Africa Cup of Nations reaching its latter stages, the United coach could be forgiven for hoping the participating nations make a swift exit.
Current injuries to captain Bruno Fernandes and Three Lions star Mason Mount only heightened the impact the absence of other forwards is having on Amorim's options.
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 suffered poor results earlier in the season.
But without them, the boss has limited alternatives in attack.
He clearly does not trust teenager Shea Lacey or the seasoned Zirkzee, even though the Netherlands forward provided the assist for the equaliser almost immediately after his introduction as a substitute.
That leaves the Brazilian, who has now scored a small tally in recent outings, and others operating out of their natural positions, alongside Sesko.
On this showing, the big-money frontman looks similar to previous struggling signings, lacking in confidence and assurance in front of goal.
His failure to turn home the cross means it is now nine games without a goal for the young striker.
After memorable victories in their previous home games, the arrival of their fiercest rivals to Elland Road was a bit drab affair.
True, there were moments of expected atmosphere, but the hostile edge was not as pronounced as in previous encounters.
The home fans were more concerned about their side's struggle to get worthwhile possession in dangerous areas for any length of time.
The Calvert-Lewin header that struck the post was an rare moment of quality in a tight first half.
It still felt as though Leeds were struggling when a mistake opened the door for the opener.
For a short moment, Leeds' delirious fans thought they were about to secure a rare win against their old foes.
However, there is a much bigger picture for Daniel Farke and Leeds to deal with.
When they endured a poor run of form earlier in the campaign, many thought about the manager's position.
In contrast, he is now masterminding significant progress.
The task is not done yet but gradually, Leeds are getting nearer to achieving their top-flight status.
Leeds have a Premier League trip to Newcastle in midweek, followed by the start of their domestic cup campaign next weekend. The Red Devils face a Premier League trip to Turf Moor before also entering their FA Cup journey with a Old Trafford tie.