Kuchar, a former Georgia Tech star who was battling an infection that made it difficult to stand up, made four bogeys through eight holes to tumble down the leaderboard, then rallied with five birdies over his last 10 holes to catch Wi, who played in the morning and shot 69.
They were at 6-under 136 and had a one-shot lead over Marc Leishman, of Australia.
Tiger Woods shot his second consecutive 72, leaving him in a tie for 40th, nine shots behind.
EUROPEAN TOUR: In Hilversum, Netherlands, Shiv Kapur, of India, shot 2-under 68 to reach 8-under and joined Nicolas Colsaerts, of Belgium, in the lead after the second round of the Dutch Open.
Colsaerts led by two shots after his first-round 62 but shot 70 in the rainy second round.
Former Augusta State golfer Jamie Elson shot 72 but missed the cut by one, finishing at 141. Gary Murphy, another former Jaguar, had 73 and finished at 144.
CHAMPIONS TOUR: In Incheon, South Korea, Fred Funk, Michael Allen and Jay Don Blake shared the lead after the rain-delayed opening round of the Champions Tour's first event in Asia.
All three shot 3-under 69 after the start was delayed by 1 hour and 39 minutes.
LPGA TOUR: In Rogers, Ark., Morgan Pressel shot 5-under-par 66 to take a one-stroke lead after the first round of the NW Arkansas Championship.
Yani Tseng, Gloria Park and Na Yeon Choi opened with 67s.
NATIONWIDE TOUR: In Sandy, Utah, Michael Putnam shot his second consecutive 66 and held a one-stroke lead after two rounds of the Utah Championship at Willow Creek Country Club.
Augusta's Scott Parel also shot 66 and is tied for seventh, four back.
Aiken's Kevin Kisner (72-73) and Stephen Poole (71-74) both missed the cut, finishing at 145. Kisner won last week's tournament.