Sluman has finished second on seven occasions since he won the 1988 PGA Championship, which remains his only tour victory.
"I feel I've played well enough since 1988 to win. Maybe the second one is a little harder than the first," he said after a five-under-par 67.
His round helped him reach a 16-under aggregate of 200, one stroke ahead of his fellow American Tom Byrum (65), while compatriots Mike Brisky (67), Fred Couples (67) and Joel Edwards (68) were two strokes behind.
Last year's US Open champion, Ernie Els, and the half-way leader Payne Stewart were among a group three shots back.