United had fired off 12 shots to nil by the half-hour mark, but a close call when Semme Lammens saved Marcus Tavernier's header from six yards out served as a warning they failed to heed. Luke Shaw was muscled off the ball by Justin Kluivert and Ayden Heaven was too slow to react to Antoine Semenyo, who then scored off the post.
Casemiro put United back in the lead before the interval, capitalising on Petrovic's botched header from Fernandes' corner, and it seemed like the game was in the bag. However, United appeared sluggish after the break.
Immediately after the restart, Tavernier's pass found Evanilson unmarked and he slotted past a stationary Lammens. Shortly thereafter, Fernandes lost possession in midfield and Casemiro was forced into a desperate tackle, conceding a free-kick 20 yards out.
Tavernier's low shot from the set piece beat Lammens, who should have been guarding that side of the goal.
As United began to look bereft of ideas, Amorim brought on Kobbie Mainoo in an attempt to salvage the situation. The thunderous applause that welcomed Mainoo's substitution for Casemiro made it clear that the Old Trafford faithful are not keen on seeing the academy graduate loaned out for the second half of the season, but the noise level soon escalated.
Fernandes redeemed himself for his blunder that led to Bournemouth's third goal by scoring a spectacular free-kick with just 13 minutes remaining. He then rallied his teammates and the crowd, demanding more urgency on the pitch.
His call was answered immediately as Mbeumo broke through a tackle, Sekso continued the attack, and Cunha capitalised on a defensive error to score his second goal for the club.
In celebration, Fernandes rushed towards the substitutes before joining his ecstatic teammates in front of the Stretford End. Cunha expressed his joy by kissing his shirt in front of the stand, igniting the atmosphere at Old Trafford.
However, the fans knew better than to take anything for granted. Junior Kroupi found room on the edge of the box and delivered a stunning finish, making Bournemouth look like the more likely victors.
In the eight additional minutes, Lammens made two crucial saves from David Brooks, preventing a disappointing night from turning into a catastrophe.