The duo is 10-under-par 132, and has a two-shot advantage over England's Gary Emerson, who shot 64 Friday, and Spain's Miguel Angel Jimenez (67), who are 8-under 134.
"I hope I can keep this up for another two rounds," said Brier. "I didn't feel too much pressure so I hope I can do another good round tomorrow and get in contention for Sunday afternoon. Maybe it's my week. I hope so."
"I have become more confident since winning," said Dyson, who captured the Indonesia Open in March.
Five-time tour winner Costantino Rocca missed the cut.