The co-leaders had a three-shot advantage at the end of another day filled with birdies in a tournament known for its low scores.
Toms shot a 7-under 65 at the PGA West Nicklaus Course, one of three used for this event, leaving him with a two-day total of 16-under 128. He is seeking his 14th career victory and his second in as many years.
Wilson, a two-time winner on the circuit last season, fired a 62 at the PGA West Palmer Course, and Crane had a 63 on the same layout.
Camilo Villegas, who shared the top spot with Toms after the opening round, posted a 68 at the Palmer course and was tied for fourth at 131 with Harris English, Chris Kirk and Bobby Gates.
Johnson Wagner, who won last week in Honolulu, was tied for 31st at 135.
Phil Mickelson, in his initial appearance of the year, had seven birdies but also made a double bogey en route to a 69 that left in him a tie for 124th at 143.