The breakthrough came in the 39th minute, with Amad curling one into the bottom corner, before Hugill came off the bench to net an excellent second for the 20-time English champions.
Man United opened their preparations for the 2024-25 campaign with a 1-0 defeat to Rosenborg last week.
However, a much-improved performance against an underwhelming Rangers led to the Red Devils securing a two-goal victory in Edinburgh.
Here, Sports Mole takes a look at three players who will have impressed manager Erik ten Hag with their displays against the Scottish giants.
Leny Yoro
Yoro only arrived at Old Trafford from Lille on Thursday, but he trained on Friday and was then named in the starting XI on Saturday, with the 18-year-old playing the first half of the clash.
The centre-back was hugely impressive, completing 44 of his 48 passes, while he had 51 touches, made two recoveries and won 100% of his duels and tackles.
Yoro showed his tackling ability with a challenge on Cyriel Dessers in the early stages, and he then produced a brilliant block on the same player late in the opening half of action.
The youngster settled effortlessly into life in the middle of the defence, making a huge impression on his first appearance for Ten Hag's side.
Amad Diallo
Amad featured in Man United's final seven Premier League matches of last season, with his standout display coming against Newcastle United, when he scored and provided an assist in a 3-2 win.
Alongside Yoro, Amad was Man United's best player in the first half against Rangers, and he capped his performance with a brilliant finish into the bottom corner.
The 22-year-old could find himself as a starter against Fulham in the team's opening match of the Premier League campaign if he continues to impress down the right.
Amad was such a huge threat to Rangers, causing a whole host of problems in a wide position, and he looked full of confidence during his 45 minutes on the field.
Jadon Sancho
Sancho, having patched-up his relationship with Ten Hag, also played the opening 45 minutes against Rangers, and he will have been pleased with his work down the left.
The forward had a brilliant chance to score during his 45 minutes of action, but he fired over the crossbar from a dangerous position.
Sancho has had clear-the-air talks with Ten Hag, with both now ready to move on from their issues, and if he can finally show his best form for the Red Devils, it will be like a new signing for the club.
A summer transfer cannot be ruled out, but at the moment, it does appear that he will be staying at the club.
Sancho helped Borussia Dortmund reach last season's Champions League final, starring against Paris Saint-Germain in the semi-finals, and this could finally be his time to star for the 20-time English champions.