The 23-year-old American two-time major winner and former world number one was sitting on a creditable three-under-par after 16 holes on Thursday when high winds and rain brought play to a premature close in California.
Rick Lamb, Noh Seung-Yul and Joel Dahmen recorded rounds of 68 to sit level at the top of the leaderboard, but Spieth will no doubt feel confident he can close the gap or even usurp them when he concludes his round on Friday.
The current world number one Jason Day is sitting alongside Jim Furyk, Shane Lowry, Seamus Power and four more players in tied for eighth, on two under after 18 holes.
Aftrer his round in tough conditions, Day said: "I feel pretty good with how things are going, coming out today and shooting a couple under par.
"The hardest part about today was actually committing to the shot more so than anything because you had a lot of side winds.
"I'm looking forward to Spyglass on Friday."
Dustin Johnson, Justin Rose and Phil Mickelson are a shot further back in 22nd place but handily placed for an assault on the leaders going into the weekend.