He fired a 10-under-par 62 in the first round of the Farmers' Insurance Open at Torrey Pines Golf Club in LaJolla Thursday.
Spence has never won a PGA Tour event, but has finished second once. He's now in his fourth season on the Tour.
"I had some putts for birdies instead of pars, and kind of added up to a good score," Levin said in his post-round news conference.
Rounds three and four will be televised this weekend on CBS.