Jon Gorenc Stankovic, who turns 19 on Wednesday, scored the only goal of the game in San Pedro del Pinatar in Spain, where Dortmund are holding their training camp.
The win should give Jurgen Klopp's men a much-needed morale boost, particularly after finishing 2014 on a four-match winless run.
New signing Kevin Kampl, who joined from Red Bull Salzburg, played a part for a Dortmund side, who had trained earlier in the day.
Stankovic struck the winner in the 59th minute, stabbing in a corner from Marcel Schmelzer.
Dortmund face Romanian outfit Steaua Bucharest on Saturday.
Sitting second bottom in the league, they resume their Bundesliga campaign with a trip to Bayer Leverkusen on January 31.
