Bayern host second-placed Dortmund on Saturday in the clash of the Bundesliga titans and with Munich playing on Wednesday night at Freiburg, Dortmund missed both the chance to shorten the gap and earn their fifth-straight victory.
Both Schalke 04 and Eintracht Frankfurt, in the pack chasing Bayern, suffered shock defeats and Bayern can go 11 points clear with a victory at Freiburg.
Dortmund coach Jurgen Klopp left out midfield stars Mario Götze and Ilkay Gundogan, plus defender Mats Hummels, who were all carrying knocks.
The move back-fired as Stefan Reisinger equalised on 78 minutes from a superb cross by Australia's Robbie Kruse after Poland captain Jakub Blaszczykowski – Kuba for short – had put the defending champions Borussia ahead on 43 minutes.
"We did not have many goal chances and we failed to convert the few we had," said Klopp. "At half-time, I told them any success Düsseldorf had was because we allowed them to counter-attack us.
"Düsseldorf should be happy with the point, they hit us very well on the counter."
Düsseldorf were reduced to 10 men when ex-Dortmund midfielder Ivan Paurevic was shown an 87th-minute red card after earning a second booking when he brought down Borussia defender Lukasz Piszczek.
After the final whistle, Fortuna's jubilant players were banned from giving interviews to German Sky Sports.
"We aren't giving Sky any interviews today, they have belittled us in the past," explained Düsseldorf's director of sport Wolf Werner, while angrily pulling captain Andreas Lambertz away from the cameras.
Schalke suffered a 3-1 defeat at Hamburg as midfielder Maximilian Beister slammed home the hosts' opener – which was recorded at 117km per hour – on 52 minutes, then helped set up Latvia striker Artjoms Rudnevs three minutes.
Hamburg defender Dennis Aogo had earlier kept his side in the game when he cleared a shot off the line while Dutch striker Klaas-Jan Huntelaar netted a 79th-minute penalty at the second attempt.
Hamburg midfielder Milan Badelj netted a 92nd-minute penalty to consign Schalke to their third defeat in their last five Bundesliga games as they remain third.
"This phase of the season, where we have so many games, is a factor, but that is no excuse," said Schalke 04 Huub Stevens, whose side have qualified for the knock-out phase of the Champions League.
Frankfurt stay fourth despite their 3-1 defeat at Mainz having been out-played and Bayer Leverkusen can jump to second from fifth if they win at Werder Bremen on Wednesday.
Hanover 96 moved up into sixth, amongst the European places, with a 2-0 win at home to second-from-bottom Greuther Fürth with goals by Senegal striker Mame Diouf and Swiss defender Mario Eggimann.
In Wednesday's other games, Borussia M'gladbach are home to VfL Wolfsburg, Augsburg are at VfB Stuttgart while Nuremberg host Hoffenheim.