Following graduation in 1995, he accepted a scholarship to play college football at Washington State in Pullman. Gleason was a starting linebacker for the 1997 team that advanced to the Rose Bowl. He was a four-year starter for the WSU baseball team in center field and holds the school record for triples.

Gleason was signed by the Indianapolis Colts as an undrafted free agent in 2000. He was released by the team after the preseason and was signed to the New Orleans Saints’ practice squad in November.

On September 25, 2006, Gleason was responsible for one of the most dramatic and memorable moments in Saints history when he blocked a punt by Atlanta Falcons punter Michael Koenen early in the first quarter of a game at the Superdome. Curtis Deloatch recovered the ball in the Falcons’ end zone for a touchdown. It was the first score in the Saints’ first game in New Orleans in nearly 21 months, during which time Hurricane Katrina had devastated the city and the team. The Saints won the game and went on to have the most successful season in their history up to that time. In September 2011, Gleason was awarded a Super Bowl ring by the Saints. At the same ceremony, he was awarded the key to the city of New Orleans by mayor Mitch Landrieu. In July 2012, Rebirth, a statue depicting Gleason blocking the punt was raised outside the Superdome.

Gleason collaborated with filmmaker Sean Pamphilon to produce a documentary on his battle with ALS that would double as a video journal for his infant son, Rivers. Included in the documentary was a 12-minute clip of Saints defensive coach Gregg Williams openly encouraging his players to injure opponents prior to a January 2011 playoff game against the San Francisco 49ers. Pamphilon released the audio recording on April 4, 2012, in the wake of the Bountygate scandal. Gleason criticized the decision, saying that he did not authorize its release.

In 2015, Gleason was chosen to receive the 2015 George Halas Award from the Pro Football Writers Association. He was presented the award at the Thursday Night Football game between the Saints and Falcons on October 15, 2015. Near the end of the first quarter, he watched as Saints linebacker Michael Mauti blocked a punt by Falcons punter Matt Bosher and returned it for a touchdown to give the Saints a 14–0 lead. Mauti, a New Orleans native and the son of former Saints player Rich Mauti, had attended the 2006 game where Gleason made his famous block. The Saints went on to beat the Falcons, 31–21. After the blocked punt, Gleason tweeted: “Hey, Falcons. #NeverPunt -SG”.

The documentary film Gleason was shown during the 2016 Sundance Film Festival. In 2019, Gleason was awarded with the Congressional Gold Medal for his contributions to ALS awareness, and became the first NFL player to receive the award. Gleason was presented with the award at a ceremony in Washington, D.C. on January 15, 2020.