The 39-year-old Portuguese was named Erik ten Hag's successor at the start of November and received a warm welcome as he led the side out in the Europa League four days on from the 1-1 draw at Ipswich.
Hojlund also set up the opening goal scored by Alejandro Garnacho in the opening minute of the game, but United still had to stage a comeback in order to stay unbeaten in the competition with two victories and three draws.
Amorim warned United would "suffer for a long period" after that first match and there were some hairy moments in his second game, but his side did enough to triumph on Thursday.
Garnacho's goal after just 48 seconds forced a first-half retaliation from the visitors, who can wrap up a fourth Norwegian title in five seasons this weekend.
Bodo struck twice in four minutes through Hakon Evjen and Philip Zinckernagel, sending their 6,500 visiting fans - 12 per cent of the city's population - wild.
But United supporters would end up celebrating in a week when the club have been roundly criticised for a new ticket pricing plan as Hojlund heeded the new head coach's plea for more goals.
The striker scored a fine volley just before half-time to make it 2-2 and turned in another early in the second half as the Red Devils secured their second Europa League win of the new-look campaign.
"I see what what everybody sees: good moments, difficult moments," Amorim told TNT Sports "There was some confusion in the end, trying to hold onto the result, but the lads did a great job.
"They ran, they pressed, they tried to do the things we have worked on in the last three days and we won."
Ange Postecoglou shouts out instructions to his players in the draw with Roma. (AP PHOTO)
In London, Tottenham's inconsistent form continued after Mats Hummels' stoppage-time goal ensured they were held to a 2-2 draw to Claudio Ranieri's Roma.
Spurs had looked on course to back up Saturday's 4-0 thrashing of Manchester City with a hard-fought victory after captain Son Heung-min and Brennan Johnson struck in the first half to cancel out Evan N'Dicka's goal.
Ange Postecoglou watched his team squander a number of chances to set up a nervy finale and not long after Fraser Forster, who deputised for the first time since Guglielmo Vicario's ankle surgery, had produced a superb save to deny Gianluca Mancini, the visitors levelled.
Postecoglou had made half a dozen changes in each of Spurs' previous four Europa League matches, but went stronger with only four from the win at Man City.
Earlier, Athletic Bilbao cruised past Elfsborg 3-0 to join Lazio and Frankfurt at the top of the 36-team standings.
Lazio missed a chance to remain the only team with a perfect record after five games as they were held 0-0 by Ludogorets at Stadio Olimpico. In Spain, Adama Boiro, Benat Prados and Gorku Guruzeta all scored for Bilbao.
Frankfurt, the 2022 Europa League winners, won 2-1 at Midtjylland.
Among other results, Jose Mourinho's Fenerbahce rebounded from their first defeat at Alkmaar (3-1) with a 2-1 win at Slavia Prague, Rangers won 4-1 at Nice, Ajax lost 2-0 to Real Sociedad and Braga eased past Hoffenheim 3-0.
In the third-tier Conference league, Chelsea moved to within one win of the last 16 with a 2-0 victory away to Heidenheim to maintain their perfect start in the competition.
Christopher Nkunku and Mykhailo Mudryk scored the goals in the second half, Jadon Sancho's cut-back shortly after the interval finding the France international who fired in his 11th of the season, before Mudryk finished things late on with a lovely finish into the top corner.
Chelsea boss Enzo Maresca mainly fielded players who are not regular starters in the Premier League where they rank third, with the London club now accumulating 12 points from their four Conference matches.
with PA
