After playing for three NHL teams across the previous two seasons, Neuvirth had a chance meeting with Philadelphia Flyers forward Jakub Voracek in the summer of 2015 that sparked the goaltender's decision to make Philadelphia his home.

Teammates on various Czech Republic national teams since they were teenagers, Neuvirth and Voracek ran into one another at the Wimbledon tennis tournament, where Voracek encouraged Neuvirth to join the Flyers.

The Flyers are glad he did. After signing a two-year contract on July 1, 2015, Neuvirth became part of the goaltending tandem (with Steve Mason) that helped lead Philadelphia back to the Stanley Cup playoffs in 2016.

Neuvirth went 18-8-4 with a 2.27 goals-against average and .924 save percentage in the regular season, then went 2-1 with a 0.67 GAA and .981 save percentage during the Stanley Cup Playoffs.

This wasn't the first time Neuvirth had performed at a high level in the postseason. As a rookie with the Washington Capitals in 2011, he finished fifth in the League in GAA in the playoffs (2.34). He also led all rookie goaltenders (minimum 300 minutes) in playoff wins (four), games played (nine), shots against (261) and minutes played (590) and was second in goals-against average (2.34) and save percentage (.912). That performance came after a regular season in which Neuvirth set a Capitals record for wins by a rookie goaltender (27) and tied Jim Carey's franchise rookie record for shutouts (four).

In 2010 he became the youngest goalie (22 years, 199 days) since Carey in 1996-97 to start a Capitals season opener. Neuvirth also tied Olaf Kolzig's franchise mark with a 10-game home winning streak during the 2010-11 season.

Neuvirth's promotion to the NHL for the start of the 2010-11 season came after he led Hershey of the American Hockey League to a second straight Calder Cup in 2010. That made him the first starting goalie since Pete Peeters of Maine (1978, 1979) to win the Calder Cup in consecutive seasons.

A second-round pick of the Capitals (No. 34) in the 2006 NHL Draft, Neuvirth won the Jack A. Butterfield Trophy as the AHL's playoff MVP in 2009.

On March 5, 2014, the Capitals traded Neuvirth and Rostislav Klesla to the Buffalo Sabres for Jaroslav Halak and a third-round draft pick in 2015. Neuvirth was traded again nearly a year later, on March 2, 2015, when the Sabres sent him to the Islanders for Chad Johnson and a third-round pick in 2016.