The 19-year-old signed for Lucien Favre's side this month for a reported fee of €20million, having been a target for Manchester United.
Haaland came on for Lukasz Piszczek after 56 minutes to make his Bundesliga debut, with BVB trailing 3-1 at the time, Florian Niederlechner scoring his second of the game after Julian Brandt had halved Augsburg's 2-0 lead.
Haaland needed only 183 seconds to make an impact, firing home a low shot after being sent through on goal by Jadon Sancho.
Sancho himself made it 3-3 and, just nine minutes later, Haaland struck again, this time tapping home from almost on the goal line after Thorgan Hazard burst through the Augsburg defence, rounded goalkeeper Tomas Koubek and unselfishly set up his team-mate.
The rising Norway star completed hit hat-trick with 11 minutes of normal time left to make it 5-3 to Dortmund, keeping his composure to side-foot beneath Koubek after being played in by Marco Reus.
IT'S A HAT TRICK FOR ERLING HAALAND!!! 🎩 pic.twitter.com/vNeAqlUxLC— FOX Soccer (@FOXSoccer) January 18, 2020