Two-time Ryder Cup player Mahan recorded five birdies in his opening seven holes en route to a round of 66 at the Pebble Beach Course in California.
Knox was playing on the Monterey Peninsula course and his six-under 64 included eight birdies and two bogeys as he and American Mahan top the leaderboard by a single stroke.
England's Greg Owen is in a tie for third alongside five other players after carding a five under par round at the Monterey Peninsula course.
The 40-year-old, who has won just one European Tour event, picked up shots on his first two holes and added three more in an unblemished round to leave himself in a good position.
American duo Matt Every and Ted Potter Jr played on the Pebble Beach course and are also on five under, alongside compatriot Scott Langley and Japan's Ryuji Imada (both Monterey Peninsula) and South Korea's Seung-Yul Noh, who was competing at the Shore Course.
England's Lee Westwood was further stroke behind after signing for a round of 68 at the end of his round on the Pebble Beach course.
The world number eight hit 10 of 14 fairways and 16 of 18 greens in regulation on his PGA Tour debut.
"My game is in good shape and there's a lot of weeks that I have not been to in the last few years that I'm looking forward to going back to again, weeks like this, Arnold Palmer's tournament, Bay Hill, the Memorial are all on the schedule," he told the PGA Tour's official website.
"So it's going to be an exciting year and hopefully a big year."