Pogge was drafted 90th overall by the Toronto Maple Leafs in the 2004 NHL Entry Draft. He began his hockey career playing with the Prince George Cougars of the Western Hockey League. Pogge subsequently wont the starting job in Prince George during his rookie WHL season, supplanting fellow Maple Leafs prospect Todd Ford, who was subsequently traded to the Vancouver Giants. Pogge was named as Prince George's Rookie of the Year for 2003-04, after not being selected in the WHL Entry Draft. Pogge split the 2004-05 WHL season between Prince George and the Calgary Hitmen, who Pogge was moved to midseason. In 2005-06, Pogge's final year in the WHL, he recorded a record of 38-10-6. Most impressive was Pogge's 11 shutouts in 54 games, as well as his 1.72 goals against average and .926 save percentage.
Pogge was signed to a contract by the Maple Leafs before the 2006-07 season, and he was sent to the Maple Leafs' AHL affiliate, the Toronto Marlies. In Pogge's first season with the Marlies, he split the games workload with J.F. Racine during the first half of the 2006-07 season. However, once it became clear that the Marlies were out of playoff contention, Pogge was allowed to take on a heavier load of games. In contrast to his 15 games played between October 2006 to December 2006, Pogge played 33 games from January 2007 until the end of the season. Pogge finished the season having played in 48 games, recording a 19-25-2 record, and a 3.03 GAA and .896 save percentage. The rookie Pogge appeared inconsistent in many stretches of games, as evident by the highs of three shutouts on the season, to the lows of six games where he gave up five or more goals.
Pogge continued to split the Marlies' schedule with another goaltender in the 2007-08 season, this time with newcomer Scott Clemmensen. The AHL sophomore Pogge appeared more composed in his second season of professional play, as he recorded a record of 26-10-4 in 41 games, while posting a respectable 2.34 GAA and .908 save percentage. Pogge also posted 4 shutouts on the season for the Marlies. Pogge has since been given the full-time starter's role for the Marlies in the 2008-09 season, as he is backed up by journeyman goaltender Adam Munro. Munro's role for the Marlies is to simply play the occasional game to relieve the physical stress of the AHL schedule from Pogge, and to prevent Pogge from being overworked.
Pogge was called up by the Maple Leafs on January 11, 2008 due to injuries faced by the NHL club. However, in his time with the team, Pogge never saw any playing time. Pogge's time with the team was short lived, as he was assigned back to the Marlies the next day.
On December 21, 2008, Pogge was once again called up by the Maple Leafs, as starting goaltender Vesa Toskala was hampered with a groin strain. Pogge made his NHL regular season debut on December 22, 2008 against the Atlanta Thrashers. He also earned his first NHL win in the game, as the Maple Leafs won the game 6-2.
Pogge has also represented Canada on the international level. Most notably, he helped the the Canadian junior hockey team to an unexpected gold medal defense of their World Junior Hockey Championship in 2006. On January 5, 2006, Pogge led Team Canada to a 5–0 win over Team Russia to win the gold medal game. After the game, Justin received the team Most Valuable Player award after facing a total of 35 shots through out the game. In 6 games during the tournament, Pogge went 6-0 with a 1.00 GAA and .952 save percentage. Pogge also recorded shutouts in 3 of the 6 games he played. His play is especially noteworthy when it is considered that Pogge was not invited to the Canadian junior summer camp prior to the tournament, and was not even expected to make the team prior to the start of the WHL season. However, Pogge's strong play with the Calgary Hitmen during the season earned him a spot on the Canadian roster.
Pogge also represented Canada at the 2006 Spengler Cup tournament in Davos, Switzerland. He took Canada to the finals, where they lost to champion HC Davos. Team Canada was coached by Pat Quinn, former head coach of the Maple Leafs.