On 11 September 2012, Karagounis left Panathinaikos to join English Premier League side Fulham on a free transfer. Karagounis became the eighth Greek player from the Euro 2004-winning side to play in the Premier League, after Nikos Dabizas, Stelios Giannakopoulos, Vassilios Lakis, Theodoros Zagorakis, Angelos Basinas and Kostas Chalkias. Speaking at Fulham's Motspur Park Training Ground, Karagounis said, "I'm delighted to have signed for Fulham Football Club and I am excited by a new challenge in England and the Premier League. I'm looking forward to working under Martin Jol and playing alongside some fantastic players at this Club." Then-Fulham manager Martin Jol added, "Giorgos Karagounis has a wealth of club and international experience and I'm happy that he's joined us for this season. He's been an influential player for his club sides and is a renowned player in world football as he's about to become the most-capped player for Greece. He brings many certain qualities to our squad."
Karagounis made his debut for the club in the Premier League on 29 September 2012, against Manchester City at Craven Cottage, coming on in the 81st minute to replace Chris Baird. Karagounis played the full 90 minutes for Fulham in their 4–0 loss to Liverpool at Anfield. He scored his first goal in England on 5 January 2013 in the FA Cup against Blackpool in the 80th minute, with a "stunning 25-yard half-volley" which went in off the underside of the crossbar; the match ended 1–1. On 12 January 2013, a week after his FA Cup strike, he scored his first Premier League goal against Wigan Athletic in the 22nd minute.
On 8 June 2012, Poland played with Greece on the opening day of Euro 2012. Poland goalkeeper Wojciech Szczęsny fouled Greek international Dimitris Salpingidis, resulting in a red card for Szczęsny. Karagounis took the penalty against substitute goalkeeper Przemysław Tytoń, who saved Karagounis' penalty.
On 16 June 2012, Karagounis started the final match of Group A against Russia, making him Greece's joint-most capped player with 120 caps, together with Theodoros Zagorakis. Karagounis scored the only goal of the match, at the stroke of half-time. This meant Greece qualified for the next stage of the competition. The second half was slightly less dramatic but had its share of talking points. Coming off a significant goal, Karagounis made a mad dash to the Russian box. The captain looked like he was going to score another, but his leg was caught by a Russian defender. Karagounis was adamant he had earned a penalty, but the referee was not impressed and booked him for simulation. Karagounis received his second yellow card of the tournament, forcing him to miss the quarter-finals.
On 12 October 2012, Karagounis played in the second half in the match against Bosnia and Herzegovina in a 2014 World Cup qualifying match, making the 121st appearance for his country. With this match, he set a new record of most caps for Greece, surpassing Zagorakis. He also scored a free-kick goal against the Liechtenstein national football team. Karagounis played another inspiring and energetic role throughout the qualifying campaign and helped lead to its third World Cup finals appearance. Despite the waning number of starts for the 37-year-old, his influence was still large for Greece. Greece head coach Fernando Santos, who worked with Karagounis at both Panathinaikos and Benfica, held him in high regard due to the sureness the veteran exudes. "We have confidence and know we can beat any opponent", Karagounis said during World Cup qualifying. Karagounis played the entire 120 minutes of the match between Costa Rica and Greece for the World Cup 2014, consisting of 90 minutes of regular time and 30 minutes of extra time.