Andrej Kramaric put the visitors ahead in the first half but Orban struck in the 89th minute to extend Leipzig's unbeaten Bundesliga run to five games
Former Leicester forward Kramaric tapped home his 10th goal of the season in the 22nd minute after a shot from Joelinton was parried by Peter Gulacsi.
Leipzig had a chance to equalise at the start of the second half through captain Orban, after a free-kick glanced off defender Kerem Demirbay, but he was denied by a great save from goalkeeper Oliver Baumann.
Hoffenheim nearly doubled their lead in bizarre circumstances when Kramaric's shot was headed by Orban straight at team-mate Marcel Halstenberg, who was on the floor, but the ball bounced off the left-back and just wide of the goal.
And Orban found a late equaliser for Leipzig, as he stretched to meet a Hastenburg cross from the left and managed to poke the ball home.