The American carded an opening round of 66 to finish five-under-par, two strokes ahead of the next closest finisher Robert Allenby, with Jeff Overton and John Peterson both five under through 15 holes.
Stanley had an inauspicious start when he shot a bogey on the first, which he went on to cancel out with a birdie three holes later.
Back-to-back birdies on the 12th and 13th, an eagle 15th and another birdie on the 17th, however, saw him card 31 on the back nine to go into the clubhouse as the early leader on day one.
Australia's Allenby had looked set to take a share of the lead, but that was derailed by bogeys on the 15th and 18th holes.
George McNeill and Alex Aragon also finished alongside Allenby on three-under, while Luke Guthrie and defending champion Jonas Blixt entered the clubhouse following an opening round of two-under apiece.
Vijay Singh recovered from a double-bogey sixth to go two-under through 17.