Emil Forsberg (left) groans after failing to convert a penalty for Leipzig at Wolfsburg on October 16, 2016
A third defeat in seven games -- with three draws and just one win -- was a disaster for Wolfsburg, who reached the Champions League's knock-out stages last season.
They are now fourteenth, just two points from the relegation places, while high-profile summer signing and Germany striker Mario Gomez is yet to score for his new club.
Sponsored by Austrian energy drinks giant Red Bull, RB Leipzig are unpopular with fans of traditional clubs, who fear the rise of corporate-backed entities in Germany's top flight.
RB were only founded in 2009, but have risen through the ranks with four promotions in seven years to reach the Bundesliga.
Their young squad, which has no big-name stars, are winning over neutral fans by playing eye-catching football, including Forsberg's superbly struck shot which curled in from outside the box on 70 minutes.
Alongside leaders Bayern Munich, second-placed Cologne and sixth-placed Hoffenheim, Leipzig are one of the few unbeaten teams in the German league.
Earlier, Mainz moved up to seventh with a 2-1 win at home to local rivals Darmstadt.
Just 48 kilometres (30 miles) separates the two clubs and while Mainz are knocking on the door of the top six, the result left Darmstadt 15th in the table, just above the relegation places.
Argentinian striker Pablo De Blasis gave Mainz the lead at the Opel Arena with a brilliant flick after just five minutes to claim his fourth goal in seven league games this season.
Darmstadt were awarded a penalty just before the break when Mainz captain Stefan Ball fouled striker Antonio-Mirko Colak, but the Croatian forward had his spot-kick saved by Danish goalkeeper Jonas Loessl.
It was a busy first-half as both sides hit the crossbar.
Mainz doubled their lead when Turkey international Yunus Malli was brought down by Darmstadt captain Aytac Sulu, but got up to bang home the spot kick on 57 minutes.
Darmstadt scored a late consolation when Mainz substitute Niko Bungert, who came on in the 90th minute, gave away a penalty for handball which midfielder Jerome Gondorf gratefully converted in injury time.
Bayern remain two points clear at the top of the Bundesliga despite their 2-2 draw at Eintracht Frankfurt on Saturday, which left the defending champions winless in their last three matches.