Sluman had seven birdies and a bogey on the 16th hole in grabbing a 1-stroke lead over Gary Hallberg and Peter Senior, who are tied for second.
Michael Allen, Jay Haas and Corey Pavin all shot 67 and are tied for fourth, two strokes behind Sluman. Defending Senior Players Championship winner Mark O'Meara is in a group of four players tied at 3-under 68.
Sluman opened with three pars before a birdie at No. 4. He pushed his way up the leader board with birdies at 6 and 7 and made the turn at 4-under after a ninth-hole birdie.
A string of birdies from 12-14 got him to 7-under but he had a bogey at the par-3 16th hole in settling for the 1-stroke lead.
Celebrity Families of 2014 [PHOTOS]