Defeat leaves City still in fifth, nine points off leaders Liverpool, who have a game in hand.
United are 13th, now within five points of their city rivals.
The Red Devils will be hoping a dramatic victory can also be the starting point for Amorim to turn around the momentum of a rivalry that City have dominated over the past decade.
Amorim made a bold call before kickoff as both Marcus Rashford and Alejandro Garnacho were left out of the United squad, with the Portuguese manager saying he “pays attention to everything”.
The United boss may have regretted that call as early as the 12th minute when Mason Mount limped off to continue his injury-ravaged spell since joining from Chelsea 18 months ago.
A shortage of confidence in both sides was clear to see in a cagey start.
It took 20 minutes for Phil Foden to have the first attempt on goal with a volley that flew just wide of Andre Onana’s goal.
But United’s set-piece defending has been at the root of their poor start to life under new management.
For the third consecutive Premier League game, they conceded from a corner as Kevin De Bruyne’s deflected cross looped perfectly into the path of Gvardiol to head in on 36 minutes.
A slow burn of a derby finally came to life seconds later when Kyle Walker and Rasmus Hojlund went head-to-head, with both ending up getting booked.
Foden’s double in this fixture for City last season put them on their way to an unprecedented fourth consecutive first division title.
The England international’s lack of form and fitness has been one of the causes of City’s struggles this season.
However, Foden looked more like his old self as a jinking run and shot that deflected just wide came close to doubling City’s lead before halftime.
United did not manage a single shot on target in the first 45 minutes and Amorim was growing visibly frustrated at his side’s poor play on the ball as the second period started in a similar manner.
A vintage City side under Guardiola would have put their neighbours to the sword, but the English champions created nothing of note in the second period.
Diallo finally forced Ederson into action with a header that the Brazilian clawed around the post on the hour mark.
Fernandes then missed a glorious chance to equalise 15 minutes from time when his dink over Ederson drifted wide with just the Brazilian to beat.
However, City were to be the architects of their own downfall.
Matheus Nunes’ short back pass played in Diallo, who was then chopped down by the Portuguese midfielder in his desperation to atone for the original error.
Fernandes this time coolly sent Ederson the wrong way to level.
City’s defence was then undone by one simple long ball over the top by Lisandro Martinez that Diallo raced on to, rounded Ederson and kept his composure to find the net.
