The South African former Open champion is level on nine under par with American Kyle Stanley, who also shot 66, with eight birdies and two bogeys.
JB Holmes spoiled an impressive round with bogeys on his final two holes to sit third overnight on seven under.
Fiji's three-time major winner Vijay Singh, 54, is fourth on six under.
He also faded at the end of his round - carding his only bogey in a 68 on the 18th.
Singh would surpass Sam Snead, who was 52 when he won the 1965 Greater Greensboro Open, as the oldest winner in PGA Tour history if he were to claim a first victory since 2008.
Ian Poulter was Britain's best performer as he followed four birdies and a bogey with an eagle on the 16th to card a 67 and move to five under. Fellow Englishman Paul Casey is one shot further back.
"I was really happy with that," Casey told Sky Sports after shooting 69.
"But I need more numbers in the 60s to catch guys like Louis at the top. Nothing really fazes him and there's a lot of depth behind too."
Rory McIlroy had two birdies and one bogey as he again failed to produce his best, carding a one-under-par 71 to move to level par overall.
After his round, the Northern Irishman said he had been suffering with a back problem.
"I'm going to get an MRI scan on Monday after the tournament and I might have to rest for a week or two," he told Sky Sports.
"As long as I get myself right for the US Open, that's the most important thing."
McIlroy's struggles were mirrored by Masters champion Sergio Garcia and world number one Dustin Johnson, who both also finished one under par, two shots above the halfway cut.
England's Justin Rose and Lee Westwood finished on one over, but their countryman Luke Donald did miss the cut, two bogeys and a double bogey between the sixth and eighth ultimately costing him as he ended on three over par.
Jordan Spieth was another high-profile casualty. The 2015 Masters and US Open champion missed the cut for a third year in a row after adding a 75 to the 72 he scored on Thursday, ending on four over par.
India's Anirban Lahiri came within a stroke of carding the highest score at the 18th hole in the tournament's history.
The world number 84 hooked three balls into the water hazard that lines the left side of the par-four hole, running up a sextuple-bogey 10.
The 29-year-old, in his second full season on the PGA Tour, shot 75 to miss the cut with a six-over total of 150.
Earlier on Friday, 2016 Masters champion Danny Willett pulled out midway through his second round because of a back injury, saying his "body and mind need a rest".
Willett, who has a history of back injuries, was 11 over par for his 27 holes in Florida.
The BMW PGA Championship takes place in Wentworth from 25 May, and asked if he would be fit to play, Willett replied: "Hopefully, touch wood.
"We'll see how things go. I've already limited the schedule down a lot. Hopefully, all going well, we get back on. We have a week to do some work and see how it feels."
BBC Sport golf correspondent Iain Carter
It has been a curious Players Championship, with none of the world's leading players fully getting to grips with a testing Sawgrass.
The 66s of Louis Oosthuizen and Kyle Stanley were exceptional rounds on a hot, breezy afternoon when the course became firmer and the water grabbed balls galore at the treacherous 17th.
Rory McIlroy made it to the weekend but it will be results of a different sort on Monday that will be more significant.
He faces an anxious wait for an MRI scan to identify the extent of his latest back injury. If rest is prescribed it may put in jeopardy his place in Wentworth's BMW PGA Championship at the end of the month.
Louis Oosthuizen shot a bogey-free six-under-par 66 to take a share of the lead after round two of the Players Championship at Sawgrass.