The young Magpies began the Premier League 2 clash against their local rivals in fine fashion, with Allan breaking the deadlock inside two minutes as the 20-year-old grabbed his 14th goal of the season with a close-range finish in front of the Gallowgate End.
Yannick Touré's glancing header doubled the hosts' advantage in the second half before the game ended in sour fashion when United forward Elias Sørensen and Sunderland captain Jack Bainbridge were both sent off following an altercation between the pair in the dying stages.
Allan said: "With it being a derby, everyone is over the moon to win but there's still stuff that we can work on. We know it wasn't the prettiest performance but, in the end, we got the job done and everybody is happy.
"There was a lot of conversations beforehand to start nice and quick and it couldn't have gone much better. Sometimes, getting an early goal can be a bit of a killer but we soaked up a bit of pressure after that and took it to them in the second half to get back into the game. After that, I thought we were pretty comfortable.
"At one-nil, it is a tricky scoreline as they are still in the game and we were a bit wary but to get the second goal settled a few nerves and we were comfortable after that.
"We're pleased to keep a third clean sheet in a row. Keeping the goals out at that end allows the lads up top to do their bit and we managed to chip in with the goals."
Allan, who made his senior debut in United's Emirates FA Cup third round replay against Rochdale last month, admitted he has been pleased with his bright form in front of goal for United's second-string.
The Newcastle-born forward, who only scored five goals during the 2018/19 campaign, has also been relishing his experience with the first-team and hopes he can continue to make good impressions with his hometown club.
He added: "I don't know what is going on this year! Everything I hit seems to be going in and today it hit my stud but I'll take it! I'm doing well at the moment so I need to keep going, trying to impress and we'll see where it takes me.
"It's been great (to be involved) with the first team. I'm taking everyday as it comes and I'm not sure if I'm with the under-23s or first team so I'm just waiting for a text on the nighttime to see what I'm doing. Everyday is good whether I'm with the first team or under-23s, I'm at my boyhood club living the dream.
"If I'm with the first team, I'm buzzing and when I'm with the under-23s, I want to do as well as I can and try to impress.
"My targets are to keep doing well with the under-23s. We want to make it to the play-offs and then, if I'm impressing, I can get more chances and try to take them too.
"Compared to last year, I'm doing a lot better and the first team training has been helping me."
