Mickelson, 50, rolled back the years to delight the home crowd at Kiawah Island as he birdied five of his last eight holes to get to five under and lead the way.
Oosthuizen then produced a wonderfully composed display to leapfrog the American before his only bogey of the day on the last left him in a tie with the 2005 champion.
There were more Major Champions at the top end of the leaderboard with 2018 and 2019 winner Brooks Koepka at four under, a shot clear of reigning Masters Tournament champion Hideki Matsuyama and Oosthuizen's fellow South Africans Christiaan Bezuidenhout and Branden Grace.
Oosthuizen's Major triumph came at the 2010 Open Championship but he has also finished second at all four of golf's biggest events.
"It'll be great to get a second Major," he said. "There's a lot of golf left and I just feel whenever I get to a Major, I sort of have my game where I want to have it and mentally I feel very strong at a Major week.
"I am definitely comfortable playing in Majors. Hitting it well and knowing your game is there, it makes it a little less stress, but you still need to hit the shots and play in the moment and play well.
"I drove it as good as I can drive it and ball striking was pretty good with the irons. With really windy conditions, you need that ball striking to be on song.
"I think I hit 14 or 13 greens around this golf course in today's conditions... pretty good."
Grace set the early pace as he made the most of the par five second and seventh, holed a bunker shot on the tenth and put an approach to five feet on the 13th to lead by two at six under.
I just feel whenever I get to a Major, I sort of have my game where I want to have it and mentally I feel very strong at a Major week
But he found the water at the 17th for a double bogey and failed to get up and down on the last after finding sand off the tee and Mickelson moved ahead.
He turned in 38 from the tenth with a birdie and three bogeys but picked up shots on the second, fourth, fifth, seventh and ninth in a 69 that left him two ahead as the afternoon starters headed out.
Oosthuizen set about reeling him in as he sandwiched a 30 footer on the fourth with smart wedges into the first and sixth to turn in 33.
He shared the lead as he took advantage of the par five 11th and an approach to 12 feet at the next meant Mickelson was no longer at the summit.
American Koepka had bogeyed the fourth and sixth but he holed a 40 footer for eagle on the next and picked up two shots again from 18 feet on the 11th.
A wonderful approach into the 12th had him in a share of the lead but he bogeyed the 15th and 17th to slip back, with Oosthuizen also dropping a late shot as he went over the back of the 18th.
Japanese Matsuyama went birdie bogey on the second and third but then picked up shots on the sixth, seventh, tenth, 11th and 13th before making a bogey on the last in his 68.
Bezuidenhout eagled the seventh from 30 feet and made a birdie on the par five 11th but dropped a shot on the 14th after missing the green off the tee.