Oosthuizen, the 2010 British Open champion, recovered from a poor start, two bogeys in the first four holes, to fire a six-under-par 64, the best round of the day at the TPC Four Seasons Resort in Irving.
"I hit the ball really well with my irons and had a lot of putts inside 10 feet for birdie and I think I made them all," the South African told CBS Sports.
Halfway leader Todd (68) also birdied the last to join Oosthuizen at 10-under 200, one stroke ahead of Canadian Mike Weir (67) and Americans Gary Woodland (66) and James Hahn (65).
Todd has never finished better than sixth on tour, while Weir, the 2003 Masters champion, has not had a top-10 finish on the U.S. circuit in more than four years.
American Morgan Hoffman was tied for the lead until he butchered the par-four 18th, yanking his drive into the water en route to a double-bogey and a 68 to fall back into a tie for sixth with, among others, Irishman Padraig Harrington.
World number 39 Oosthuizen pulled out of last year's Byron Nelson Championship after three rounds, due to a neck injury, and he also battled back problems earlier this year.
However, a runner-up finish at the Malaysian Open last month indicated he was back in form.
Oosthuizen, whose smooth swing is regarded by his peers as one of the best in the game, said he liked the course this week because it puts a premium on accuracy rather than power.
"It's so tough out of the rough," he said. "The key thing for me is hitting fairways and then finding greens, because I'm putting really well.
"I putted really well today, putted well yesterday, so I want to give myself as many birdie opportunities as I can (tomorrow) and make a few."
Seventeen-year-old American Scottie Scheffler became the first amateur since 2006 to record a hole-in-one on the PGA Tour when he aced the par-three second with a five-iron from 218 yards.
It was the sixth hole-in-one on tour this year.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Mark Lamport-Stokes)
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