Key Moments
The Red Devils' poor run of form persisted at Elland Road, but head coach the Portuguese tactician had his Brazilian forward to thank for the team not suffering even more damage against Leeds.
The Everton loanee directed a first-period effort against the post for the confident home team before the American midfielder finished superbly with a low, 62nd-minute effort.
With the goal, Amorim was in the firing line after his side had failed to beat struggling Wolverhampton Wanderers at home earlier in the week.
However, against a team who had two days less to recover, Cunha restored parity three minutes after the opener when he latched onto a pass from substitute the Dutchman and guided a finish underneath rushing Leeds goalkeeper Lucas Perri.
It was only the Brazilian's fourth goal since his big-money summer move and came at a time when Amorim is without four key attacking players due to a mix of injury and national team commitments.
Not that you would expect Leeds to sympathise with that given their own lack of preparation time.
Noah Okafor forced a full length save out of visiting goalkeeper Senne Lammens with a spectacular overhead kick, and United heads were in hands when the Slovenian striker, who is finding it hard to make an impression, 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 match, also blasted against a post late on.
The point prolongs the home side's unbeaten run to seven games, their longest such streak since 2001, and takes them eight points clear of the drop zone.
For the visitors though, it was yet another chance to move into the Champions League places, albeit only for a matter of hours, wasted.
With the Africa Cup of Nations reaching its knockout phase, Amorim could be understood for hoping the involved countries make a swift 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 the team's squad.
It's not that the missing pair are the solution to all of United's problems. After all, they were part of the side that experienced disappointing results earlier in the season.
But without them, Amorim has few alternatives in attack.
He clearly does not trust teenager Shea Lacey or the much more experienced Zirkzee, even though the Dutch forward provided the assist for Cunha's equaliser almost immediately after his arrival as a substitute.
That leaves Cunha, who has now scored three goals in five games, and others playing out of their natural positions, alongside Benjamin Sesko.
On this showing, the big-money frontman looks no better than previous underwhelming 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 last few home games, the arrival of their fiercest rivals to Elland Road was a comparatively subdued affair.
True, there were moments of expected fervor, but the hostile edge was not as evident as in other encounters.
The home fans were more preoccupied about their side's struggle to get sustained possession in advanced areas for any length of time.
The striker's header that clipped the post was an isolated moment of threat in a tight first half.
It still felt as though the hosts were struggling when a mistake opened the door for the opener.
For a short moment, Leeds' ecstatic fans thought they were about to secure a rare win against their old foes.
Nevertheless, there is a much bigger picture for Daniel Farke and the club to deal with.
When they endured a difficult run of form earlier in the season, many speculated about the manager's future.
In contrast, he is now masterminding clear progress.
The job is not completed yet but gradually, the team are getting nearer to securing their survival.
Leeds have a top-flight trip to St James' Park in midweek, followed by the start of their domestic cup campaign next weekend. The Red Devils face a league trip to Turf Moor before also beginning their FA Cup journey with a home tie.
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