Wi, 39, took full advantage of Toms' torrid third round to lead overnight and maintained his place at the head of the leaderboard after completing his front nine on one-under par, 14-under overall.
The South Korean birdied the first two holes before dropping shots on the fourth and sixth, although an impressive birdie putt on five kept him under par.
Toms managed to regroup after his third-round 74 on Saturday saw him lose his grip on first place, and he made par on the opening six holes before picking up a shot on the par-four seventh.
Australian Stuart Appleby finished his front nine on four-under par to remain the only other likely challenger, as it left him in third and only a shot behind Toms.
Last year's winner Zach Johnson had completed his final round, carding an impressive 65 to leave him on nine-under par for the tournament.
Toms had started his third round with a commanding lead of seven shots after successive rounds of eight-under 62 - which matched Pat Perez's scoring record for the first 36 holes of a tournament set in 2009.
And on Saturday he appeared on course to continue that form as he opened with a birdie, but successive bogeys on the second and third started to derail the American.
He endured two further bogeys, as well as a double bogey on the 14th, while sinking just one more birdie.
Toms said: "I felt after the first six holes, I was just hanging on, trying not to make a mistake. Maybe I'll go out there with a little pressure off of me and see if we can do better on Sunday."
Wi had gone out in two-under, then was a bogey-free two-under coming in as he sought his first PGA Tour title.
John Senden was then third at nine-under, four strokes off Wi's lead of 13- under. Alex Cejka was the leading European in a five-way tie for 12th after a four-under 66 while Scotland's Martin Laird was back in a share of 17th.