Career
Before playing in the NHL, Haula played one season with Omaha Lancers of the United States Hockey League (USHL) and three years with the Minnesota Golden Gophers of the Western Collegiate Hockey Association (WCHA). He had a successful time with his teams. With the Gophers, he was named to the All-WCHA Second Team.
He was drafted 182nd overall by the Minnesota Wild in the 2009 NHL entry draft. On 7 April 2013, Haula signed a two-year, $1.8 million entry-level contract to join the Wild. He was sent down to play for their AHL-affiliate Houston Aeros.
On 29 November 2013, the Wild called him up and Haula made his NHL debut in a 3–1 loss against the Colorado Avalanche. During the game, he recorded his first NHL point by assisting on a Dany Heatley goal. On 8 October 2013, Haula scored his first NHL goal against Kari Lehtonen in a 3–2 overtime win against the Dallas Stars. On 2 August 2015, Haula signed a two-year, $2 million contract to stay with the Wild.
On 21 June 2017, the Wild left Haula unprotected in the 2017 NHL expansion draft and he was selected by the Vegas Golden Knights. The same day, Haula signed a three-year, $8.25 million contract to stay with the Knights. He helped the Knights when they went on a run in the playoffs. They defeated the Los Angeles Kings, San Jose Sharks, and Winnipeg Jets on route to their first Stanley Cup Final appearance in Golden Knights franchise history. They were eventually defeated by the Washington Capitals four games to one in the Finals.
On 26 June 2019, the Knights traded Haula to the Carolina Hurricanes in exchange for Nicolas Roy and a 2021 conditional fifth-round draft pick. He scored 12 goals and recorded 10 assists for 22 points in 41 regular season games for the Hurricanes.
On 26 June 2019, the Hurricanes traded Haula along with Lucas Wallmark, Eetu Luostarinen and Chase Priskie to the Florida Panthers in exchange for Vincent Trocheck. He played 7 regular season games and recorded 2 assists, as well as, 4 playoff games where he scored 1 goal.
On 23 December 2020, Haula signed a one-year, $1.75 million contract to join the Nashville Predators. He played one season with the Predators.
On 28 July 2021, Haula signed a two-year, $4.75 million contract to join the Boston Bruins. He played one season with the Bruins.
On 8 July 2022, the Bruins traded Haula along with to the New Jersey Devils in exchange for Pavel Zacha. He played parts of three seasons with the Devils.
On 18 June 2025, the Devils traded Haula back to the Nashville Predators in exchange for Jeremy Hanzel and a 2025 fourth-round draft pick.
Finland