Singh, who shot a 5-under 67, and Hart, who shot a 4-under 68, had a two-stroke lead at 9-under 207 through 54 holes.
Dustin Johnson posted a 68 and Michael Allen a 71 Saturday to tie for third at 7-under 209. Ryan Armour (68), Y.E. Yang (68), Steve Lowery (70), Fredrik Jacobson (70), Jeff Quinney (71) and Jason Day (71) were tied at 6-under 210.
Among the best 16 rounds Saturday, only two -- Jim Furyk's 67 and Greg Owen's 68) -- were played at the third host course, Poppy Hills.
The fourth and final round Sunday will be played at Pebble Beach.
Defending champion Phil Mickelson, who won by five shots last season, missed the cut by six this year after turning in a 78-221 Saturday at Pebble Beach.