It was a second successive flop for Amorim's side following their 4-3 League Cup quarter-final exit at Tottenham on Thursday.
Bournemouth took a first-half lead through Dean Huijsen before Justin Kluivert and Antoine Semenyo netted after the interval to complete a dismal afternoon for Amorim, who replaced the sacked Erik ten Hag in November.
A year after securing their first ever victory at Old Trafford, Andoni Iraola's Cherries triumphed by the same scoreline as they inflicted the biggest blow of Amorim's short reign.
Huijsen became the latest player to capitalise on United's woeful set-piece defending, before a Kluivert penalty and a Semenyo strike sealed a stunning win that brought boos from the home fans at full-time.
The result leaves United marooned in 13th over Christmas and marked an alarming fall from grace after last Sunday's 2-1 derby win at Manchester City.
Amorim had always warned there would be bumps in the road but a fourth defeat in his ninth match in charge further underlined the issues.
"This game was hard on us. We suffered again on set-pieces and we were a bit nervous. I felt it in the stadium," Amorim said.
"If we manage to score the first goal then the game should be different. We want to score but we are too nervous. We have to fight this.
"After the penalty, we need to control the game better because we know this situation is really hard. We have to control better this moment.
"We have to focus on the job and not what you feel in the stadium. It's the only way I know how to focus my players. We have to suffer again but we will try to win. We will do it until the end."
Rashford exile
Marcus Rashford's absence from a third consecutive matchday squad had dominated the pre-match discussion as Amorim made six changes.
Rashford has said he is ready for a "new challenge", sparking talk that he will be sold in the January transfer window.
But, asked if Rashford could return to the team at Wolves on December 26, Amorim would only say: "It depends, we will see.
"I always expected the job to be tough, especially in these busy months. We are ready to face the challenge."
United offered little attacking threat without Rashford and their glaring deficiences at the back were ruthlessly exploited by a Bournemouth side who are now up to fifth place.
Tyrell Malacia was furious to be adjudged to have fouled Adam Smith and Huijsen easily beat Joshua Zirkee to head home the resulting free-kick from Ryan Christie in the 29th minute.
Amorim brought on Leny Yoro for Malacia at half-time and soon made two further changes, with Rasmus Hojlund and Alejandro Garnacho replacing Zirkzee and Manuel Ugarte.
The changes made no difference and Noussair Mazraoui conceded a careless penalty when he brought down Kluivert in the 61st minute.
The Netherlands international stepped up to send Andre Onana the wrong way as he stroked home from the spot.
United's capitulation was complete two minutes later.
Kobbie Mainoo's pass was cut out and Bournemouth broke as Evanilson slipped in Dango Ouattara, whose cutback was driven home by Semenyo.
Jubilant Bournemouth fans chanted "Man United, it's happened again" in reference to last year's victory, while the dejected home supporters flooded towards the exits.
