On Saturday, he did it again.
The 35-year-old Greece captain scored the opening goal in the opening match against host Portugal at the 2004 European Championship, exploiting a slip in defence to mark the start of a seemingly impossible run to the title.
Beating the odds once more, Karagounis scored Saturday against Group A favourite Russia at Euro 2012, kicking in the game's only goal seconds before halftime. The skilful Russians couldn't find a way back as Greece coach Fernando Santos stifled them with an unyielding defence that denied them space with a playing formation that looked like a stack of bricks.
Greece made the quarterfinals, and the timing could hardly have been better.
The Greeks had looked doomed to another early exit, compounding gloom in a country that votes in a general election Sunday under the weight of financial and political crisis.
"We're not Brazil, but we're a team that fights. I thank God that we can live such moments, unforgettable moments," Karagounis said. "We were so determined. We played with heart and passion because we wanted to make Greeks happy."
The Greece playmaker equaled a national appearance record of 120 games set by for captain Theo Zagorakis five years ago.
"Playing the way we did is more important than getting to 120," said Karagounis, often referred to as "the Dude" in the Greek media because of his good nature. "I think we deserve more respect, to play this way against the odds, and never give up."
A crowd and team favourite, Karagounis debuted for Greece at 22 years old and remains one of his country's most frequently selected players, featuring in all 10 Euro 2012 qualifiers.
On Saturday, he scored his ninth international goal after a career spent mostly at Panathinaikos but also at Inter Milan and Benfica.
"We'd been winding him up all day before the game about the appearance record," Greek football federation president Sofoklis Pilavios said. "For Giorgos to get that goal on his 120th cap made everyone happy. ... We are so proud of the players. It's hard to describe what they've done."
Karagounis has earned a reputation as a dogged playmaker, skilful on assists and dead-ball chances, good for team morale, and — with a stuntman's knack for collapsing to the ground — earning free kicks.
Most of all, fans identify with his emotion.
The Greece captain thought he won a penalty in the 61st minute again Russia after making contact with a defender in the area, but instead was booked for diving. In disbelief, Karagounis crossed himself repeatedly and six minutes later he was substituted.
"It was a clear penalty. UEFA should check the video," said Karagounis, who will miss the quarterfinal match but still struggled to contain his excitement at Greece advancing.
"We decided it was too early to go back home. All the players said it. And we kept our promise," Karagounis said. "When you fight together no one can stop you."