Match Summary
The Red Devils' disappointing run of form persisted at Elland Road, but head coach Ruben Amorim had his Brazilian forward to thank for the team avoiding even more damage against their old rivals.
Dominic Calvert-Lewin headed a first-period attempt against the post for the in-form hosts before the American midfielder applied a cool finish with a driven, 62nd-minute shot.
At that stage, the United boss was under intense scrutiny after his side had failed to beat struggling Wolverhampton Wanderers at home earlier in the week.
Nevertheless, against a team who had less time to prepare, Cunha restored parity three minutes later when he latched onto a through ball from substitute the Dutchman and guided a finish underneath rushing Leeds goalkeeper Lucas Perri.
It was only the Brazilian's fourth Premier League goal since his high-profile summer move and came at a time when the manager is without four key attacking players due to a combination of fitness issues and national team commitments.
Not that you would expect Leeds to sympathise with that given their own tight schedule.
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 the Slovenian striker, who is finding it hard to make an impact, turned Zirkzee's cut-back wide from close range.
Cunha, who had a goal disallowed for offside much earlier in the match, also blasted against a post in the dying moments.
The draw prolongs the home side's unbeaten run to seven games, their best such streak since over two decades ago, and takes them eight points clear of the drop zone.
For the Manchester United though, it was yet another opportunity to move into fourth spot, albeit only for a matter of hours, squandered.
With the AFCON reaching its latter stages, the United coach could be understood for hoping the participating nations make a pretty quick exit.
Existing injuries to skipper Bruno Fernandes and England international Mason Mount only exacerbated 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 United's problems. After all, they were part of the side that suffered disappointing results earlier in the campaign.
But without them, the boss has few attacking options.
He evidently does not have full faith in youngster Shea Lacey or the much more experienced Zirkzee, even though the Dutch forward provided the assist for Cunha's equaliser almost immediately after his introduction as a substitute.
That leaves the Brazilian, who has now scored a small tally in five games, and others playing out of their preferred positions, alongside Benjamin Sesko.
On this evidence, the big-money frontman looks no better than previous struggling signings, lacking in belief and conviction in front of goal.
Sesko's 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 biggest rivals to home was a bit drab affair.
True, there were instances of expected atmosphere, but the intimidating edge was not as evident as in other encounters.
Leeds' fans were more concerned about their side's inability to get sustained possession in dangerous areas for any length of time.
The striker's header that clipped the post was an rare moment of quality in a congested first half.
It still felt as though Leeds were struggling when a defensive error 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.
However, there is a wider context for the manager and the club to deal with.
When they suffered a poor run of form earlier in the season, many thought about the manager's position.
In contrast, he is now overseeing significant improvement.
The job is not completed yet but gradually, Leeds are getting nearer to securing their top-flight status.
The Yorkshire club have a top-flight 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 cup journey with a Old Trafford tie.
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