Ian Madigan scored a penalty to win with the last kick of the game at the BT Murrayfield Stadium.
Dan McFarland's side will now face Leinster in the final.
THAT. MOMENT! 🙌@Ian_madigan 🔥 pic.twitter.com/Y7OjjDyEIv
— Ulster Rugby (@UlsterRugby) September 5, 2020
It comes as Edinburgh lead Ulster 12 points to no score after just over 50 minutes of the game.
Tries by Chris Dean, Darcy Graham and Stuart McInally gave Richard Cockerill's side a 19-7 lead.
However, Ulster managed to make a recovery, with Ian Madigan's 80th-minute penalty securing the final victory.
𝔽𝕌𝕃𝕃-𝕋𝕀𝕄𝔼
WHAT. A. FINISH!!!!
Ulster book their place in the #GuinnessPRO14 final to face @leinsterrugby next weekend! #EDIvULS #GuinnessPRO14 #SUFTUMLive ⚪️🔴 pic.twitter.com/WS8arDKo5y— Ulster Rugby (@UlsterRugby) September 5, 2020