Match Summary
The Red Devils' disappointing run of form persisted at Leeds' fortress, but head coach Ruben Amorim had his Brazilian forward to thank for his side avoiding even more damage against their old rivals.
Dominic Calvert-Lewin headed a first-period effort against the woodwork for the in-form home team before Brenden Aaronson finished superbly with a low, 62nd-minute effort.
At that stage, Amorim was under intense scrutiny after his side had failed to beat bottom-of-the-table Wolverhampton Wanderers at home earlier in the week.
Nevertheless, against a team who had less time to recover, Cunha levelled three minutes after the opener when he ran on to a pass from substitute the Dutchman and guided a shot underneath advancing home goalkeeper Lucas Perri.
It was only the Brazilian'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 injury and international duty.
Not that you would expect the hosts to care about 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 United heads were in hands when the Slovenian striker, who is struggling to make an impression, turned Zirkzee's cut-back wide from close range.
Cunha, who had a goal ruled out for offside much earlier in the contest, also fired against a post late on.
The point extends 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 visitors though, it was yet another chance to move into fourth spot, albeit only for a matter of hours, squandered.
With the Africa Cup of Nations reaching its knockout phase, Amorim could be understood for hoping the participating nations make a pretty quick 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 Amorim's squad.
It's not that the missing pair are the answer 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, the boss has few attacking options.
He evidently does not trust youngster Shea Lacey or the seasoned Zirkzee, even though the Dutch forward delivered the assist for the equaliser almost instantly after his arrival as a replacement.
That leaves Cunha, 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 no better than previous underwhelming signings, lacking in confidence and assurance 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 thrilling victories in their previous home games, the arrival of their biggest rivals to home was a comparatively subdued affair.
True, there were moments of typical fervor, but the hostile edge was not as pronounced as in other encounters.
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 struck the post was an rare moment of quality in a congested first half.
It still felt as though Leeds were finding it tough when a defensive error opened the door for the opener.
Ever so briefly, Leeds' delirious fans thought they were about to secure a rare win against their old foes.
Nevertheless, there is a wider context for Daniel Farke and Leeds to deal with.
When they suffered a difficult run of form earlier in the campaign, many speculated about the manager's position.
Instead, he is now masterminding clear improvement.
The job is not completed yet but gradually, the team are getting nearer to achieving their survival.
The Yorkshire club have a top-flight trip to Newcastle 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 entering their FA Cup journey with a home tie.
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