The 21-year-old Taylor shot a 5-under 66 Monday to take a one-shot lead over Nick Geyer, who played at the University of New Mexico.
Taylor, an All-America from the University of Washington, had six birdies and a bogey at the Jimmie Austin Golf Course on the University of Oklahoma campus.
Rickie Fowler, of Oklahoma State, is among a group of four tied for third with 68s.
The second round of qualifying is Tuesday then the top 64 advance to match play.
The winner earns a spot in the Masters.