Overnight pacesetter Henley fired a three-under-par 67 at Waialae Country Club in Honolulu while fellow American Langley carded a 65, the pair posting a tournament low of 17-under 193 after 54 holes.
The two 23-year-olds, each making their first starts as US Tour members, will take a three-shot lead over South African Tim Clark (66) into Sunday's final round.
Australian Scott Gardiner (65) and American Charles Howell III (67), who has twice been a runner-up at Waialae, were a further stroke back at 13 under in a tie for fourth place.
"Whatever happens tomorrow, I'm going to learn from it," Henley told reporters after playing in the company of Langley for a third day in a row.
"I've played great golf and I feel like I can compete out here. Win this tournament or not, it's already been a very successful week."
Henley and Langley, who shared low amateur honours when they tied for 16th at the 2010 US Open, eclipsed the previous 54-hole record set by John Huston with 194 at the 1998 Sony Open.
Two strokes in front at the start of another warm and breezy day at Waialae, Henley maintained that advantage with birdies at the second and eighth before Langley trimmed the lead to one with a two-putt birdie at the par-five ninth.
Left-hander Langley picked up another shot at the 10th to draw level at the top, then forged one ahead when he coolly sank a 12-footer from the fringe at the par-four 13th.
A three-putt bogey at the 14th dropped Langley back into a tie for the lead but he immediately regained a one-stroke cushion when he rolled in a 14-footer to birdie the 15th.
His playing partner Henley signed off with a two-putt birdie at the par-five last to become the first player to reach 17 under par after 54 holes at the Sony Open.
Moments later, Langley had a golden chance to improve that record by one but he lipped out with his birdie attempt from 11 feet and had to settle for dual honours and a share of the lead.
Victory for either player on Sunday would emulate the achievement of fellow American Garrett Willis, who was the most recent rookie to win on his debut as a US Tour member -- at the 2001 Tucson Open.
- Sports & Recreation
- Waialae Country Club