The Norwegian struck twice in the first half after Bevis Mugabi was shown a straight red card for the hosts inside 60 seconds.
Melkersen headed home Sylvester Jasper’s cross on the quarter-hour mark before making an excellent run, control and finish to double the advantage.
Melkersen, who lasted 75 minutes before being replaced by Christian Doidge, took in the adulation of the Hibs support at full-time. He could scarcely have made a better introduction on his first start for the club after a couple of substitute appearances.
"It's amazing, it can't get any better. There were so many Norwegian flags,” said the 19-year-old.
"I knew I would have to be patient to develop into the team. I just needed to stay calm and wait for my chance. You see today, I've had a good game.
"I've just done extra sessions every day and listen to the coaches, I try to do the best I can do, then you get results.
"I've always had that in me, so I just need to continue.
"It was a huge moment to come to Scotland. I enjoy Edinburgh and it can't get any better with the fans.”