"I tell you what, you make me feel bad about it," Courier replied. "Look at you, 35 years old playing like that, get out of here Roger Federer. We'll see you in a couple of nights."
Federer fans were biting their nails as he approached the court to play world No.10 Tomas Berdych in the third round.
The Swiss master put on a masterclass in the first two sets, displaying his former finesse as he worked his opponent around the court.
If there was any fault in the 35-year-old's match, it was being easily broken by Berdych's powerful baseline play in the third set - but it didn't seem to bother the world No.17 too much.
Federer blasted his way through to take the win in straight-sets, a feat that saw him escape a looming 16-year low in his career.
If he lost in the third round, Federer's ATP ranking would have dropped out of the top 30, a region not seen by the former champion since January 2001.
He will now take on Kei Nishikori in the fourth round, a prospect Federer says he's looking forward to.
"I guess I'm ready now," he said. "There's no turning back now, so I like Kei. I've always been a fan of his game, he's a nice kid. He's had a great few seasons, last year I followed him closely.
"I remember when he was 17, we played in Japan, I don't know, he's just a good guy. I'm happy to play against him.
"He has maybe the best backhand in the business now, I've got my work cut out. I hope I can play a good match."
