The motivation of both sides to kickstart their respective seasons with a result here was clear in a first half which had everything but goals.
The action started with a fabulous volley from Lisandro Martínez which was palmed away from the corner by Bernd Leno, before United’s strong spell culminated in Bruno Fernandes knocking it against the post from Cunha’s pull-back.
But Fulham responded by peppering their opponent’s goal with attempts, first when Alex Iwobi looped a cross over to Josh King at the far post, but his shot was too close to Senne Lammens.
The Belgian international stopper was on hand again to keep out a rasping effort from Sander Berge, before Oscar Bobb pulled wide following a brilliant turn past Martínez.
King’s next shot, right footed across goal after Iwobi’s pass, was also toed away by Lammens, while a long shot from Cunha took a deflection off Berge and forced Leno to tip the ball onto the post at the other end.
A couple of wayward efforts from Marcus Rashford, still looking for his first goal since returning to United, completed a remarkable tally of 26 total first-half shots, the most in any PL match so far this season.
That trend completely reversed at the restart though, with over 15 minutes elapsing before the first attempt of the half, but the opener nevertheless came shortly afterwards.
Calvin Bassey wrestled it off Cunha and stormed towards goal, his shot being saved by Lammens but then calamitously poked by Martínez into his own net.
Leno made sure that strikes from both Bryan Mbeumo and Cunha didn’t find the net as United rallied to respond, but there was little he could do about the equaliser with just moments of normal time remaining.
Cunha’s hit from distance took a heavy deflection off David Affengruber and rolled into the net, well clear of Leno’s trailing leg for the Brazilian’s fifth career H2H goal.
There were fears among the home crowd of United completing their turnaround, but Fulham held firm for a point.
Their side nevertheless miss out on what would have been just a second win in 22 top-flight meetings with United, while the Red Devils can’t avoid equalling their lowest-ever points tally after five matches of a season in the PL era.
Flashscore Man of the Match: Senne Lammens (Manchester United)