Pierre-Emerick Aubameyang's brace was not enough to salvage a point for the leaders as their 41-match unbeaten home run in the Bundesliga came to a dramatic end.
Both teams were reduced to 10 men before the hour while penalties were awarded at either end, but Leipzig ultimately held their nerve in a pulsating encounter.
Having only given up two goals in their previous seven league outings, Bosz was in no doubt over the cause of the hosts' downfall.
"We played too many backwards balls - that is not our game - and we defended badly," the Dutchman said after the match.
"We had a lot of trouble with Leipzig's pressing, particularly in the first half.
"We tried to change that in the second half but then we went 3-1 behind and the red card happened."
Victory moved the visitors to within three points of Bosz's men, who are now only two clear of champions Bayern Munich.
Leipzig boss Ralph Hasenhuttl attributed his team's barnstorming performance to their "brave" dedication to attack.
"I'm very proud of how we performed. We wanted to put on a spectacle," Hasenhuttl said at his post-match press conference.
"We always believed in ourselves and we really put [Dortmund] under pressure. I said before the game it would be back and forth and that is how it worked out.
"In the end we deserved the victory."