McGirt is just the 26th player to record two eagles in one round during The Players Championship and just the sixth to do so on back-nine at TPC Sawgrass.
The two have a one-shot lead over Rahm, veterans J.B. Holmes and Chez Reavie and rising Swedish star Alex Noren.
Overnight joint leader Oosthuizen also began his round with a bogey, and the South African was inconsistent all day as he dropped three further shots while making two birdies in an erratic 74.
"I'm not going to lie, it wasn't a great day out there", Garcia told the Golf Channel.
Mackenzie Hughes was 5-for-5 in scrambling, and lost his drive right at the 470-yard, par-4 18th hole, leaving himself nearly blocked out from 207 yards.
"You don't know whether to say "be good", "go" or "sit" because it's such a tricky hole, but it was a pretty good yardage for me to hit a solid 52-degree (wedge) and fortunately it worked out flawless for me and went in".
Garcia seized his long awaited Major title by winning the U.S. Masters last month and now has his eyes set on the PGA Tour's flagship event where the Spaniard is five-under-par and just four shots off the lead.More news: Pippa Middleton marries as royals look on
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"This is a golf course where I've had to rein in my game over the years", McIlroy said.
Since the inception of the Players Championship in 1974 no player has successfully defended the title, with only six managing to win the prestigious event a couple of times. McGirt followed that up with another eagle on the 16th after a handsome second shot got him to within 10 feet of the cup.
"It happens. I played some good golf out there today, just unfortunately not on the last two".
He made it sound simple, even though the Players Stadium Course can be anything but that. He showed up for the first time in 2014 at age 20 and not only did he share the 54-hole lead with Martin Kaymer, he played 58 holes before making his first bogey. "I had some good results last week, and yeah, it was just one of those days".
Sergio Garcia was nervous and distracted during much of the first round Thursday of The Players Championship. "But there's so many unknowns because we don't even know, unless you get an image taken of it and you know exactly what's going on you don't know". "I've already limited the schedule down a lot, obviously all of the travelling we've been doing, and everything that's been going on". Sweltering heat doesn't hurt, and the four-time major champion assured himself of two more rounds at the TPC Sawgrass after navigating the firm conditions and endless water hazards with two birdies in his round of 71.
Day was playing in the same group as Rickie Fowler, the 2015 champion who also got off to a fast start until one bad shot - a really bad shot - on his 15th hole at the par-4 seventh. "An under-par round will be key to get back in it".