Wi, who started the day at the Colonial Country Club seven strokes behind first- and second-round leader Toms, registered five birdies and only one bogey to finish 54 holes at 13-under-par 197.
Wi is seeking his first PGA Tour title.
Toms, meanwhile, faltered to a 4-over 74, falling behind by one stroke at minus-12. Toms was also the 36-hole leader last at The Players Championship but eventually lost in a playoff to K.J. Choi.
John Senden (70) was a distant third at minus-9.
Stuart Appleby (67), Paul Goydos (67) and Mark Wilson (71) were knotted in fourth place at minus-8.
Saturday's third-round action was delayed for 80 minutes by rain.
Duggar sisters unveil Christian dating rules in new book
Beautician charged with giving client fatal silicone butt injection