Aron Price, the Livermore Valley Wine Championship winner, is one stroke back at 5 under and he was joined there by Gary Christian, Marc Leishman and Miguel Angel Carballo.
Levin, 22nd on the money list, ran off three consecutive birdies from the second to get his round going. After four consecutive pars, Levin converted a birdie effort on the ninth to make the turn at 4 under.
Around the turn, Leishman followed a 45-foot eagle putt on the par-5 12th with a birdie on the 13th at Midland Country Club.
However, he tripped to a bogey at the 14th after losing his tee shot to slip back to minus-six. He parred out for a share of the lead.
'It was a real good bogey though,' Levin admitted. 'I lost my ball and had to re-tee it.'
Gillis, who got into the field via the Monday qualifier, played the back nine first. He also made eagle on the 12th and followed with birdies at 14 and 15.
After three pars, Gillis birdied the first to move to 4 under. He drained back-to-back birdie tries from the fourth, but followed with a bogey at the sixth. Gillis birdied the seventh, but dropped another shot on the eighth to finish at 6 under.
'I love this place. I always have a special feeling when I come here because you have to flight your ball,' said Gillis. 'The wind blows and you have to hit shots. I love playing golf like that.'
Edstrom, who has missed the cut in seven of his last eight starts, also had a chance to lead by himself after the first round, but tripped to a late bogey. He made eagle at the par-5 fourth.
After a pair of pars, Edstrom birdied the seventh. He got to 4 under with a birdie at the 10th.
Edstrom poured in three straight birdies from the 12th to jump into the lead at minus-7. He parred the next three before stumbling to a bogey at the last that cost him the outright lead.
Brendon Todd is alone in eighth at 4-under-par 68. Fabian Gomez, Jon Turcott, Won Joon Lee, Michael Boyd, Ryan Howison, Ricky Barnes and Joe Daley are one stroke back at minus-3.