Stuard wound up second in Mexico during one of the tournaments played prior to the new year that count toward the tour's 2014 campaign.
He ranked 10th on the tour's money list coming into this event and he shot his second straight 65 at the Waialae Country Club for a 10-under-par 130 total. His Friday round was highlighted by an eagle at the par-5 ninth hole.
Stuard has yet to win on the tour.
Marc Leishman shot a 64 and Hideto Tanihara had a 65, leaving them tied for second at 131. Harris English was alone in fourth at 132 while the group at 133 included Adam Scott and first-round leader Sang-Moon Bae.
Jordan Spieth, runner-up to Johnson a week ago, missed the cut after shooting a 71 that included a tee shot that went out of bounds at the first hole.
UPI horse racing weekend preview
Bo Jackson: I can't help Jameis Winston anymore