The 20-year-old attacker has been touted as a potential superstar since the age of 15 but his reputation as a difficult talent to manage saw him struggle to get his professional career going.
The Cameroon-born forward, who can operate up front or out wide, has flourished this season at Basel after joining on loan from Red Bull Salzburg and it has taken just a few months for him to re-establish his reputation as a special talent capable of reaching great heights.
A quick, skilful and impulsive player whose best position is hard to define, Oberlin is already playing below his level according to some.
"If Oberlin had done everything right, today he would be at one of the 10 best clubs in Europe,” Remo Gaugler, Basel team planner, says of a player who rejected the chance to join United's Under-18s a few years ago and turned down Bundesliga hot shots RB Leipzig too.
A key part of a Basel side who are pushing for second place in their Champions League group, his first full season in senior football is shaping up to be a great breakthrough year.
Oberlin often plays up front or on the wing, where he holds his position when Basel defend deep in their own half, but his great pace and directness see him move into the centre high up the pitch where he is most threatening.
He tends to go straight to top speed, as if the sprint button is always down on his FIFA 18 controller, and it often hinders him as he loses control and allows defenders to stop him at decisive moments.
When it goes well, though, he can produce magic.
After clearing a corner from the six-yard box against Benfica this season, he raced upfield at mind-blowing speed to get behind the last defender, take on a through ball and slot past Julio Cesar. It was an exceptional goal and the highlight of his integral role in the 5-0 Champions League win.
Earlier, the Switzerland U21 international Injected pace into a Basel attack when he stole it from a team-mate on the wing, burst into the centre and set up a shot with a nice pass. He then rushed in to square the rebound for Michael Lang to open the scoring.
He made it a perfect 20th birthday in the second half when he pounced on a terrible pass and knocked the ball beyond the initial tackle, relying on his great acceleration to get back on track to fire home.
The youngster also looked bright in a 30-minute substitute appearance against CSKA Moscow. He made it 2-0 in the 90th minute when he took on a pass and beat the keeper, but only a few seconds after blasting a glorious opportunity over the bar, among other missed chances.
His record of six goals in 17 games in all competitions is good for a player in and out of the starting XI, and he is clearly still a raw talent. His three goals in four Champions League game shows he is more effective when Basel are playing a more counter-attacking style than in the Super League, where opponents sit deeper.
Oberlin has been inconsistent as a result, but Basel boss Raphael Wicky sees value in his erratic style even at his worst.
“I don’t think [he is frustrating],” he told Basler Zeitung. “Because no matter how Dimi plays, always and everywhere in the box he offers me one thing: a high degree of intensity.
“Players like Oberlin don’t always know themselves what will happen next. They act instinctively. That makes them unpredictable, this sometimes causes nerves, but above all it is a strength. Dimitri will become calmer and clearer as he grows with experience.”
The support Basel have given him has provided a stability he has lacked over most of his career so far.
He moved from Cameroon to Switzerland at the age of nine with his younger brother to be with his mother and stepfather. At 14, he joined a village team and was referred to as a “godsend” and a “serpent” by his coach as he slithered past opponents.
He soon went to Zurich where he was prolific in the youth team, attracting an offer from Manchester United, and making his first-team debut at 16, playing one minute in the last game of the season.
The next campaign passed him by as he grew frustrated with his place in Zurich’s reserves despite the growing attention from other teams and soon left the club.
Austrian side Red Bull Salzburg snapped him up in 2015 and although he scored in his second league game and made a few substitute appearances, he was dropped to their feeder club Liefering in the second tier.
He knocked RB Leipzig back to spend 2016-17 on loan at Austrian Bundesliga side Altach, where a record of nine goals in 21 games helped propel them to the top of the league at the turn of the year.
Salzburg’s decision to recall him in January sparked accusations they were just weakening a rival by taking away their best attacker, but his improvement had indeed been noted and he scored on his first game back. After a few more appearances, he suffered an injury and was ruled out for six weeks.
"Oberlin is very sensitive, an extraordinary player who needs exceptional support. He needs affection and space. If you give it a lot, you get a lot back,” Altach sporting director Georg Zellhofer told Neue Zurcher Zeitung.
Basel have so far found a good balance for Oberlin and made a smart move in taking him with an option to buy as he is showing more of his potential. The player has been vindicated, too, in his decisions to reject Man Utd and RB Leipzig along the way to chase first-team football at a good level.
“Oberlin moves somewhere between genius and madness,” Swiss newspaper Aargauer Zeitung declared.
At this rate, we will likely see much more of the former as he develops.