The first round was delayed for over two hours as an electrical storm threatened Laguna National Golf & Country Club. Play was ultimately called for darkness.
Fowler vaulted out of the gate with birdies on each of his first four holes, but found trouble with a bogey at the par-5 seventh.
The Australian dropped another shot with a bogey at the ninth, but managed to recover on the inward half. Fowler ran off three birdies on the back nine for his share of the clubhouse lead.
'I took the week off last week and needed it,' said Fowler. 'Frankly it wasn't enough, but I will put everything into this week then take another four weeks off.'
Levet tallied back-to-back birdies starting at the par-4 fourth and added a birdie at the 10th to reach 3 under.
The 35-year-old picked up another birdie at the 13th and played his approach to 18 feet at the par-four 16th. Levet then drained the birdie putt to move to minus-5.
'My game is in good shape and my putting was much more solid than of late,' said Levet. 'I've got no worries about my long game and it's been a case of being patient and waiting for the putting to come.'
James Kingston got to 7 under on his round before a costly triple-bogey at the par-3 eighth, his 17th, dropped him back to minus-4.
'I over-clubbed at the eighth with a 6-iron and it went into the water and I took a triple,' said Kingston. 'To make one mistake like that is very frustrating.'
Kingston was joined in the clubhouse by Peter Lawrie, Peter Hanson, Gregory Hanrahan, Kyi Hla Han, Yuan-Chi Chen, Jong-Duk Kim, Wen-Tang Lin and Arjun Singh at 4-under-par 68.
Defending champion Lian-Wei Zhang, who received an invitation to become the first Chinese golfer to compete at the Masters next month, converted a five-foot birdie putt at the ninth, his last, to complete a round of even-par 72.