The 19-year-old -- who joined Borussia Dortmund from Red Bull Salzburg this month -- scored two goals from the bench on Friday night in Dortmund's 5-1 hammering of FC. Koln.
Raphael Guerreiro, Marco Reus and Jadon Sancho grabbed the other goals as Dortmund moves back up to third in the Bundesliga table.
The Norwegian striker's double takes his tally to five goals in his first two games for his new club.
Having started on the bench on his debut against Augsburg, he came on to score a second-half, 23-minute hat-trick in a 5-3 victory.
It means that Hland's five goals have come in his first hour of football in Germany.
He also broke a Bundesliga record with his two goals, as no previous player had scored five goals in their first two appearances in the German top flight.
"It's simply wonderful -- five goals, two games, there are worse starts," said Dortmund captain Marco Reus after the win.
Hland caught the attention of top European clubs this season after scoring 22 goals in 18 appearances for Salzburg, including four hat-tricks in the Austrian top flight and the Champions League.
English giants Manchester United was heavily linked to acquiring his signature and sealing a reunion with Hland's former manager at Norwegian club Molde and current Manchester United boss, Ole Gunnar Solskjaer.
And after choosing Dortmund over Manchester, football journalist Richard Jolly highlighted what the Premier League club missed out on, saying: "Erling Braut Haaland has scored more league goals than Manchester United in 2020 (5-4). Haaland has played 57 minutes. United have played 360."
Hland has scored a hat-trick in all four competitions he's played in this season -- the Austrian Cup, Champions League, Austrian Bundesliga and German Bundesliga.
Dortmund now sit level on points with reigning Bundesliga champions Bayern Munich and four behind current leaders RB Leipzig, who has a game in hand.
Alongside his new teammate, England international Sancho also broke a Bundesliga record. At the age of 19 years and 305 days, he became the youngest player to score 24 Bundesliga goals.