Christian Atsu put the visitors ahead as early as the third minute, but seven minutes later Zwolle were level through Guyon Fernandez.
It looked as though both sides would have to settle for a share of the points until Patrick van Aanholt claimed a last-minute winner to send his team to the summit as Zwolle's wretched run of form in the league continues, their last win coming on October 20, nine games ago.
Peter Bosz's side are now three points clear of Twente, who beat Heracles on Friday night, and Ajax, who host PSV on Sunday.
Steven Berghuis scored twice, in the 23rd and 69th minutes, either side of Aron Johannsson's goal in first-half stoppage time and Breda have now won just once in their past six league outings.
Elsewhere, RKC Waalwijk and Groningen drew 1-1, Michael de Leeuw's opener for Groningen cancelled out by Evander Sno's penalty eight minutes from time.
