Burke, Scotland’s most expensive player following his £13 million move from Nottingham Forest, came off the bench and fed fellow substitute Naby Keita to grab the only goal of the game with one minute remaining, sparking wild celebrations among the home fans.
It was RB Leipzig’s first ever Bundesliga win after they won promtion to the top fight for the first time last season.
World Cup final match-winner Mario Goetze was expected to dominate the headlines on making his second debut for Dortmund following his move from Bayern Munich. But it was Scotland winger Burke who had the bigger impact.
The result will send shockwaves through the German game and annoy many of the country’s traditionalists.
Leipzig are unpopular among rival fans who see the club as a marketing tool for energy-drink manufacturer Red Bull.
Opponents resent their commercial side and short history. The club was founded in 2009 when Red Bull rebranded fifth-tier side SSV Markranstaedt and financed their speedy promotion as a new entity through the lower leagues.
Some Dortmund fans refused to travel to Leipzig for the game, which was nevertheless sold out. Leipzig sporting director Ralf Rangnick said the club could have sold twice as many tickets.
It is the first time the former East Germany has had a top-flight club since Energie Cottbus was relegated in 2009.