Stuttgart's win over Freiburg on Friday ensured Dortmund slipped to 18th ahead of their trip to the Commerzbank-Arena, where Jurgen Klopp's side paid the price for two defensive errors in the weekend's final game.
Last season's runners-up were sent on their way to an eighth league defeat of the season after just four minutes when Matthias Ginter and Neven Subotic failed to deal with a long clearance - Alexander Meier taking full advantage.
Klopp was without the likes of Marco Reus, Mats Hummels, Ciro Immobile and Sokratis Papastathopoulos, with an injury for Lukasz Piszczek before the break compounding Dortmund's frustrations.
Things got worse for the visitors late on when a defensive mix-up between Ginter and goalkeeper Roman Weidenfeller allowed Haris Seferovic to wrap up the win and move Frankfurt up to ninth.
Wolfsburg have taken on Dortmund's mantle as the nearest challengers to Bayern Munich and they kept pace with the leaders courtesy of a 1-0 win against Borussia Monchengladbach.
After Pep Guardiola's Bayern picked up maximum points against Hertha Berlin on Saturday, Dieter Hecking's men were able to stay in touch by condemning Monchengladbach to a third consecutive Bundesliga defeat.
Robin Knoche's strike 12 minutes in was enough to get Wolfsburg back on track after defeat to Schalke last time out and move back within seven points of Bayern.
"My team has delivered an outstanding performance and through their commitment and strength in the duels earned the victory," coach Hecking told the club's official website.
"Unlike [in the UEFA Europa League defeat to Everton] on Thursday we also had luck on our side."
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