Stallings made four birdies and an eagle before darkness suspended play, and is at 18 under for the tournament.
The 27-year-old is trying for his second career PGA Tour victory. He’ll continue his round this morning at 8 a.m.
Billy Horschel, Heath Slocum and Jason Bohn are tied for second place at 14- under.
The tournament has been plagued by heavy rain, with one weather-related delay during each of the first three days.
Only a handful of players finished their third round on Saturday, including William McGirt.
McGirt shot 8-under 64 and is the clubhouse leader at 13-under 203, or five strokes behind Stallings.
Augusta pro Patrick Reed is at 204 after 66. Reed, who opened the tournament with 73, is now 11-under for his past 36 holes.
On Saturday, Reed bogeyed the first hole, then struck for birdies on Nos. 2, 5, 7, 10, 16, 17 and 18.
The former Augusta State All-American had four birdies in the first round but had seven in both the second and third round.