For the first time in their history, the Red Devils have lost both league matches against Palace in a single season after they produced a woeful display in Monday's clash at Selhurst Park.
Michael Olise and Jean-Philippe Mateta grabbed a goal apiece to leave Man United trailing by two goals at the interval.
Tyrick Mitchell added a third in the 58th minute, before Olise netted his second Palace's fifth to condemn Erik ten Hag's side to a demoralising loss.
Man United experience worst defensive season in 47 years
After shipping four goals at Selhurst Park, Man United have now let in a total of 81 goals in all competitions this season.
That tally represents the highest number of goals conceded since they shipped the same amount in the 1976-77 campaign.
They have also failed to keep a clean sheet in 10 consecutive Premier League away matches since they played out a goalless draw with Liverpool in December.
Casemiro operated as a makeshift centre-back alongside Jonny Evans in Monday's defeat, and it ultimately proved to be a forgettable night for the experienced Brazilian.
The 32-year-old was dribbled past on eight occasions at Selhurst Park, which is a record high for a Premier League match in the 2023-24 season.
Highest number of losses in 34 years
Having lost 13 of their 35 Premier League matches, Man United have now suffered the highest number of league defeats in a single season since they lost 16 games in 1989-90.
Those poor results have contributed to a total of 18 competitive defeats in the current campaign, which is the most they have suffered since they lost 19 matches in all competitions during the 1977-78 season.
Man United now have a fight on their hands to secure European football, with the Red Devils sitting in eighth spot and two points adrift of Newcastle United.
They will clinch a Europa League if they beat Manchester City in the FA Cup final, while a defeat to their rivals would create another European place in the Premier League.