Roared on by the usual raucous Alexandra Palace crowd, the Singapore veteran stunned Dutch-born Swede Jeffrey de Graaf.
The previous oldest player to win a round was Northern Ireland's John McGowan in 2008, when he was 67.
Lim will face former world champion Luke Humphries next, a player he beat at the tournament five years ago.
"So I hope on a given day it can happen again, but I never give up. He is good, but he can be beaten," Lim, known as the Singapore Slinger, said after his 3-1 win.
Lim's longevity has made him one of the most iconic names in darts, and in 1990, he became the first player to hit a world championship nine-darter at the BDO tournament.