Els said the course "played probably the fairest of the last couple of days" on Saturday.
As for his eagle, he said he was pin-high chipping to a green that was angling toward him.
"I was in the first cut in the little fringe there, a beautiful lie, and I guess it was almost a 50-yard shot," he said. "So it's one of those one-in-a-thousand shots."
Els, who finished about 90 minutes ahead of the final pair, said he at least wanted to be within four strokes of the lead entering Sunday's final round.
"That's a great chance, I feel," he said. "I think if you get it into the red numbers, I think you'll win this tournament somehow. I know it's saying a lot at 2-over but red numbers will win."
If there was one thing you could say about 17-year-old amateur Beau Hossler in the third round, it's that he just wouldn't go away.
The resolute Hossler, who held the lead briefly during the second round, followed each of his four bogeys with a birdie on the very next hole, carding a 70 for a 54-hole score of 213 that left him in a tie for eighth place.
"To bounce back like that is huge," said Hossler, who is entering his senior year at Santa Margarita (Calif.) High School. "You can easily get on the bogey train out here but making the birdies really salvaged the round."
Phil Mickelson couldn't find much at Olympic to make his 42d birthday a happier occasion, carding a 1-over 71 for a 54-hole total of 8-over 218.
Mickelson, a five-time Open runner-up, was even-par for the day after a birdie at the 12th but couldn't find another birdie the rest of the way. He bunkered his approach at No. 18 and wrapped up the day with a bogey.
At least he could appreciate the fans singing "Happy Birthday" to him.
"It's a long, difficult day, even though it's my birthday," he said. "And it was very flattering of the fans, thank you."
Peterson's an ace
John Peterson, the 2011 NCAA champion who is in his first year as a professional, recorded a hole-in-one at the 181-yard 13th hole.
Peterson, 23, a former LSU star who was playing in the next-to-last group with David Toms, used a 7-iron for the memorable shot. He reacted joyfully when the ball disappeared into the cup. He exchanged a poorly executed chest bump with his caddie and was high-fived by Toms.
Peterson finished with a 72 for a 213.
Contact Joe Juliano at 215-854-4494 or firstname.lastname@example.org or follow him on Twitter @joejulesinq. Read his blog, Golf Inq, at www.philly.com/sports/golfinq