The American produced a bogey-free seven-under 63 to be clear of countrymen Peter Malnati and Billy Horschel at the TPC Southwind.
Horschel is one of several players unable to complete their rounds, with darkness stopping play when the 27-year-old was through 16 holes.
It came after poor weather saw the opening round delayed by three-and-a-half hours and officials will be eager to finish as planned on Sunday with the US Open starting next week.
Crane was in fine form, starting on the back nine with five birdies before holing another couple on the front nine to lead.
A bogey on the par-four 17th hole meant Malnati slipped two shots adrift, while Horschel has the eighth and ninth still to play.
Horschel eagled the par-five third, getting on the green in two before sinking a nine-foot birdie putt.
A group of five players are at four under and tied for fourth, including South African Retief Goosen (66) and American Joe Durant (66).
Jason Bohn and Zach Johnson are among them through 14 and 15 holes respectively, while Australian Stuart Appleby has one to play.
American Phil Mickelson (67) is one of 14 players at three under, alongside Swede Freddie Jacobson and Troy Merritt.
Merritt was set for a better round before finding the water off the 18th tee and ending his day with a double bogey.
Englishman Lee Westwood managed an even-par 70, while defending champion Harris English (73) made a slow start.
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