Few would have predicted such a win for United at San Mames Stadium - which will host the Europa League final on 21 May.
Indeed, initially it did not look likely with some of the visiting players appearing nervous.
Manuel Ugarte was often caught in possession in the opening 15 minutes, while a static defence was almost embarrassed when Inaki Williams rose highest to glance a header over.
Patrick Dorgu was caught way up the pitch to allow Inaki Williams space to attack and deliver a cross for Alex Berenguer, whose shot was blocked on the line by Victor Lindelof.
The loud atmosphere created by the home fans undoubtedly contributed to those nervous displays from United's younger players but their senior players stepped up to ultimately settle them.
Brazil midfielder Casemiro rolled back the years with a display reminiscent of his Real Madrid days, sitting deep to break up attacks, offering composure and creativity on the ball while also providing an aerial threat.
Harry Maguire, criticised previously for being past his best, scored the late winner against Lyon in the quarter-finals, and popped up on the right wing this time to deliver the cross that led to Casemiro's the opener.
Then there was captain Bruno Fernandes, who was coolness personified to shut out the noise of the stadium and convert the penalty that put United in control, before dinking home a second when played through on goal.
Amorim was full of praise for his senior players for providing the calming influence.
He told TNT Sports: "You can feel especially in the beginning player like Ugarte with a lot of experience was a bit nervous, also Patrick Dorgu.
"These kind of players like Casemiro, Harry Maguire and Bruno Fernandes help a lot."