The world No 82, trailing 5-4 overnight against 2015 world champion Stuart Bingham, slipped to a 10-7 defeat at the Crucible.
But Carty impressed against the Masters champion, even if there were no fans to cheer him on inside the empty theatre.
Bingham had struggled on Friday, and was fortunate to lead 5-4, but he moved up a couple of gears on Saturday morning.
Breaks of 109, 96, 57 and 58 put Bingham 9-4 in front, needing just one more frame to secure a last-16 spot.
But Carty - who only turned professional in 2018 - showed his potential, responding with breaks of 83, 51 and 56 to cut the deficit to 9-7.
Bingham was visibly wobbling, but held his nerve with an 82 break to secure victory.