The win is Man United's first in the competition this season, and it has seen them move up into 15th spot in the Europa League table on six points, while PAOK sit 33rd, collecting just one point from their first four matches.
Man United had a strong shout for a penalty in the first period when Amad went down under contact from Baba Rahman, but the referee was not interested and VAR somewhat controversially agreed with the on-field decision.
The Red Devils were the team looking the most likely at Old Trafford, with Amad arguably the biggest threat, but PAOK were defending well and also had their moments down the other end, with Man United goalkeeper Andre Onana needing to make a brilliant save late in the first period to keep out a powerful strike from Mady Camara.
Man United had 58% of the possession in the first period but managed just one shot on target from four attempts, with PAOK actually the more productive outfit in the final third, having two shots on target from five attempts.
The breakthrough did arrive early in the second period, though, with Amad brilliantly heading a deep Bruno Fernandes cross into the back of the net, and there was immediately a sense of relief inside the stadium.
PAOK had a golden chance to level the scores just past the hour when Tarik Tissoudali found himself free inside the box, but the striker somehow fired his effort straight at Onana.
Amad then doubled Man United's lead in the 77th minute, with the Ivorian brilliantly curling the ball into the far corner of the net after wrestling his way into a shooting position.
Interim head coach Ruud van Nistelrooy now has just one more game at the helm, with Leicester City the visitors to Old Trafford in the Premier League on Sunday, before Ruben Amorim arrives from Sporting Lisbon next week.
MAN UNITED VS. PAOK HIGHLIGHTS
Amad Diallo goal vs. PAOK (51st min, Man United 1-0 PAOK)
Man United make the breakthrough in the 51st minute of the match, and it is a wonderful header from Amad, as he guides a deep Fernandes cross into the back of the net. Incredible header from the Ivory Coast international!
Amad Diallo goal vs. PAOK (77th min, Man United 2-0 PAOK)
Man United have their second of the match, and it comes from Amad, with the attacker working his way into a shooting position before curling the ball into the far corner. What an excellent goal from Man United's number 16!
MAN OF THE MATCH - AMAD DIALLO
Amad was the best player on the pitch at Old Trafford, with the Ivorian putting in an eye-catching display; the former Atalanta BC youngster was Man United's standout performer in a largely disappointing first period, and he then made the breakthrough with an excellent header in the early stages of the second half.
The 22-year-old then scored a brilliant second in the 77th minute, and he had five shots in total, while the forward also made three tackles and won three aerial duels during an all-action performance at Old Trafford.
Man United vs. PAOK MATCH STATS
Possession: Man United 53%-47% PAOK
Shots: Man United 16-8 PAOK
Shots on target: Man United 4-4 PAOK
Corners: Man United 9-2 PAOK
Fouls: Man United 10-15 PAOK
WHAT NEXT?
Man United's attention will now switch back to the Premier League and what will be Van Nistelrooy's final game in charge of the Red Devils before the arrival of Amorim; that fixture comes against Leicester on Sunday afternoon, and the 20-time English champions will be eyeing just their fourth league win of the campaign.
PAOK, meanwhile, will continue their Greek Super League campaign with a clash against Olympiacos on Sunday night; the reigning Greek champions are currently second in their domestic table, one point behind the leaders Aris Thessaloniki.