Jones also tamed Spyglass with a 66 in brilliant sunshine to join 2014 champion Snedeker at 12-under 131, one stroke ahead of American Justin Hicks, who shot 68 at Monterey Peninsula.
Australian Jason Day, coming off a playoff victory last Sunday, shrugged off a stomach bug to vault within three shots of the lead with a nine-under 62 at Monterey Peninsula.
Snedeker, a six-times PGA Tour winner, has slipped outside the top 50 in the world rankings and is not exempt for the Masters in April, something he wants to rectify with a win on Sunday.
"It's no fun not being eligible for the Masters, so it's a huge motivating factor," he told reporters.
"I definitely want to make sure I qualify for the Masters (and World Golf Championships events) and to do that I need to play good."
Snedeker is looking forward to moving to the host Pebble Beach course for the final two rounds, after getting Spyglass out of the way.
"Around Spyglass, you're just trying to get out of there without too much damage," he said.
"It's a tough course and I played really well. My wedges have been great the first two days and I've been rolling the ball really well."
The 34-year-old knows he will have to keep making birdies to emulate his victory of two years ago.
"Scores are a lot lower than when I won. I've got to shoot something under par, pretty low, because conditions are perfect."
Jones, meanwhile, said an early par had been the key to his good score.
"Fifth hole probably kept my round going," said the Houston Open champion. "I hit a terrible tee shot and was able to get up-and-down for par, and from there kept going."
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)
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