Gudļevskis started his professional career in the 2009–10 season playing for HK Ogre of the Latvian Hockey League. In the next season, he moved on to play for Dinamo Riga affiliate HK Rīga of the Minor Hockey League (MHL). He played for three seasons with HK Rīga. Throughout the 2010–11 and 2011–12 seasons he made the Dinamo Riga roster several times as a healthy scratch. On 5 October 2012, he finally made his debut during a 2–1 overtime win against Vityaz Chekhov, replacing injured Mikael Tellqvist after the second period tied at 0–0. Later in the season he played his first full game as starter in a 2–0 loss against Sibir Novosibirsk.

Gudļevskis was recalled to the Syracuse Crunch of the AHL on 24 October 2013, due to an injury to Riku Helenius. He made his AHL debut on 26 October 2013, with a shutout against the Bridgeport Sound Tigers. Gudļevskis became the fifth goaltender in Crunch history to post a shutout upon debut. After four games with the Crunch, Gudļevskis once again was reassigned to the Everblades. On 7 December 2013, Gudļevskis was promoted to the Syracuse Crunch in order to give him more AHL ice time. Gudļevskis cemented his place on the Crunch roster posting 10 wins in 21 games. On 15 January 2014, Gudļevskis was named the CCM/AHL Player of the Week.

Gudļevskis became the starting goaltender for Team Latvia in the 2013 IIHF World Championship after original starter Edgars Masaļskis could not recover game form coming from injury. He registered 2–2 win-loss record and was named one of three best players for Team Latvia in the tournament.

On 31 January 2014, due to injuries of Ben Bishop and Anders Lindbäck, Gudļevskis received an emergency call-up to the Lightning along with Cédrick Desjardins. Kristers made his first NHL start on 11 April 2014, in a game between the Lightning and the Columbus Blue Jackets, he stopped 36 shots in a 3–2 win for the Lightning. He made his NHL playoffs debut after replacing Lindbäck mid-game on 18 April 2014, against the Montreal Canadiens in the second game of the first round. He replaced Lindbäck in game four of the series as well. During this season, Gudļevskis became the first goalie in the history of the sport to play in an ECHL, AHL, NHL and Olympics in the same season, which also included his Stanley Cup playoffs debut.

On 7 January 2014, Gudļevskis was named to the Latvian national team roster for the Sochi 2014 Winter Olympics. Latvia entered the qualification playoff stage ranked as one of the lowest seeds (ahead of only Norway), amassing no points in group play. In the second round, Gudļevskis got the start in the matchup against reigning Olympic champions Canada, despite the Latvian team upsetting Switzerland earlier with goalie Edgars Masaļskis.

On 10 June 2015, in game four of the 2015 Stanley Cup Finals against the Chicago Blackhawks, Gudļevskis became the back-up goalie for fellow prospect Andrei Vasilevskiy, who started the game after Ben Bishop was injured in game two (Bishop played injured in game three).

On 24 October 2015, Gudļevskis played in his second NHL regular season game against the Chicago Blackhawks, stopping 31 shots. Though he had a great effort, he lost in overtime 1–0, when a backhand shot slipped by taken from Jonathan Toews.

On 2 July 2016, the Lightning announced the re-signing of Gudļevskis to a one-year, two-way contract. Gudļevskis played in 41 games with the Syracuse Crunch in the 2015–16 AHL season, posting a 16–12–8 record with a 2.83 goals-against average and a .907 save percentage.

On 1 July 2017, Gudļevskis was traded by the Lightning to the New York Islanders in exchange for Carter Verhaeghe. On 11 July 2017, Gudļevskis signed a one-year, two-way contract with the Islanders. In the following 2017–18 season, Gudļevskis was assigned to AHL affiliate, the Bridgeport Sound Tigers for the duration of the year. In splitting starting duties, he recorded 12 wins in 37 games.

As an impending restricted free agent with the Islanders and with his NHL career stalled after five seasons in North America, Gudļevskis opted to return to home in agreeing to a one-year deal with former club, Dinamo Riga of the KHL, on June 21, 2018.He was released on 1 October 2019, after posting a 3.45 GAA and a .863 save percentage in just 9 games.

On 2 December 2019, he signed a contract with the Fischtown Pinguins of the DHL.