Woltemade made his debut for the Magpies after joining from VfB Stuttgart, where he was set up by Jacob Murphy to score the only goal in the 29th minute.
This achievement makes Woltemade the third German player to score on his Premier League debut, following in the footsteps of Jurgen Klinsmann, who achieved this in August 1994, and Ilkay Gundogan, who scored in September 2016.
Woltemade will look to build on this success when Newcastle faces Barcelona in the Champions League on Tuesday.