Carl Paulson, David Sutherland, New Zealand's Craig Perks and Paul Gow of Australia shared second place on 66.
Shaun Micheel, Australia's Stuart Appleby, Thomas Levet of France, Neal Lancaster, Kent Jones, Chris DiMarco, Garrett Willis, Heath Slocum, Hunter Mahan and Jason Buha were all a stroke further back on 67.
US Open winner Jim Furyk and British Open champion Ben Curtis led a group of 12 players on four-under 68 while world number one and defending champion Tiger Woods carded a 69.
The eagle came at the par-four 12th when he holed out from 110 yards with a wedge.
"I have not been playing well up until last week," Sposa told reporters.
UNLIKELY CHAMPIONS
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Sposa, yet to win on the tour, said he had been encouraged by the run of unlikely champions in recent weeks.
Curtis won the British Open two weeks ago while Craig Stadler and Peter Jacobsen have become the sixth and seventh oldest players to win PGA Tour events.
Curtis, the PGA Tour rookie who is making his first start since winning at Sandwich, began on the back nine and went out in a three-under 33.
He added two more birdies before a bogey at the par-three eighth dropped him back to four-under for the day.
Paulson was paired with Sposa and said the two fed off each other's momentum.
"You see a guy going well and you say 'Doesn't make any sense why I can't make any birdies'," said Paulson. "Kind of frees you up a little bit."
Woods, who earlier this week switched drivers from a Nike to an old Titleist because he was not shaping his tee shots the way he wanted, hit only eight of 14 fairways.