Minnesota Wild

On 7 April 2013, the Minnesota Wild signed Haula to an entry-level contract.^[2] During the 2013–14 season on 29 November 2013, the Wild recalled Haula from the Iowa Wild of the American Hockey League (AHL) to make his NHL debut, where he scored first NHL point, an assist, and he was named the game's third star in a 3–1 loss to the Colorado Avalanche.^[3][4] On 9 December, Haula was reassigned to Iowa.^[5] In his return to Minnesota, on 18 January 2014, Haula scored his first career NHL goal against the Dallas Stars in the first period. During 2014 Stanley Cup playoffs, he scored four goals and three assists in 13 playoff games.

Following the 2014–15 NHL season Haula became a restricted free agent under the NHL Collective Bargaining Agreement. The Minnesota Wild made him a qualifying offer to retain his NHL rights and, on 27 July 2015, Haula filed for Salary Arbitration.^[6]

The 2015–16 season saw a breakout year for Haula, as he set NHL personal bests in goals, assists, and points, more than doubling his previous highs in all three categories. He centered Minnesota's third line with Nino Niederreiter and Jason Pominville, quickly becoming Minnesota's most effective line offensively as well as acting as a shutdown line against the league's best.

Vegas Golden Knights

At the completion of his fourth season with the Wild in 2016–17, as a restricted free agent Haula was left exposed for the 2017 NHL Expansion Draft. After agreeing to a three-year, $8.25 million deal with the Vegas Golden Knights, Haula was Minnesota's required selection for the draft on 21 June 2017. In exchange for selecting Haula, the Knights received prospect Alex Tuch and sent a conditional third-round pick in 2018 to the Wild.^[7] When speaking of his new team, Haula said: "Nothing has happened [in Vegas] before. Everything is new. It's a great opportunity for everybody, so you just start building from there...I'm really excited for this opportunity in my career."^[8] However, on 14 October, Haula suffered a lower-body injury and was expected to miss at least one week.^[9] After missing four games, he returned to the Golden Knights lineup on 27 October for a contest against the Colorado Avalanche.^[10] Upon returning to the Golden Knights, Haula was moved around the lineup and centered a line between David Perron and James Neal, resulting in an increased output.^[11] During the month of December, Haula and teammate William Karlsson each recorded seven goals, which tied for the eighth-most in the league.^[12] On 1 February, Haula scored a goal to help the Golden Knights set a record for most wins by an NHL team in its inaugural season.^[13] He ended the regular season with a career-high 29 goals for 55 points through 76 games.^[14]

Following his career-high regular season, Haula and the Golden Knights faced off against the Los Angeles Kings in the first round of the 2018 Stanley Cup playoffs.^[15] During Game 1, Haula ended the longest game in the franchise's history by scoring the second overtime game winning goal to give the Golden Knights a 2–1 win over the Kings.^[16] The Golden Knights eventually swept the Kings in four games to qualify for the second round.^[17] During Game 1 against the San Jose Sharks, Haula, Cody Eakin, and Jonathan Marchessault all scored goals within 1:31 of each other in the first period.^[18] The Golden Knights eventually beat the Sharks in six games to advance to the Western Conference Final,^[19] where they beat the Winnipeg Jets in five games.^[20]

Haula returned to the Golden Knights for the 2018–19 season without his previous linemates, Perron and Neal.^[21] As a result, Haula was moved to the wing position on the teams' second line with Max Pacioretty and center Paul Stastny.^[22] While playing on this line, he sustained a right leg injury when he was hit by Toronto Maple Leafs forward Patrick Marleau and was expected to miss three games.^[23] At the time of the injury, Haula had recorded two goals and five assists in 15 games.^[24] However, it was later revealed he would need a few months to recover and was placed on injured reserve.^[25] In December 2018, Haula underwent surgery on his right knee.^[24]

Carolina Hurricanes

On 26 June 2019, Haula was traded by the Golden Knights to the Carolina Hurricanes in exchange for prospect Nicolas Roy and a conditional fifth-round draft pick.^[26] Haula then started the 2019–20 season with eight points through nine games and was praised by teammate Jordan Martinook as being a "perfect fit".^[27] By November, Haula had tallied 11 points in 16 games to place fourth on the Hurricanes in goals before missing four games with a lower body injury.^[28] Upon returning to the lineup, he centered Brock McGinn and Brian Gibbons on the team's fourth line.^[29] He returned for two games before being named out indefinitely on 18 November due to a knee injury.^[28] Haula subsequently missed 15 games before returning on 21 December for a 4–2 loss to the Florida Panthers.^[30]

Florida Panthers

As an impending free agent, Haula was dealt at the NHL trade deadline by the Hurricanes along with Lucas Wallmark, Eetu Luostarinen and Chase Priskie to the Florida Panthers in exchange for Vincent Trocheck on 24 February 2020.^[31]

Nashville Predators

On 23 December 2020, approaching the delayed 2020–21 season, Haula signed as a free agent in agreeing a one-year, $1.75 million contract with the Nashville Predators.^[32] He recorded 9 goals and 21 points in 51 games of the shortened season.

Boston Bruins

As a free agent at the conclusion of his contract with the Predators, Haula was signed to a two-year, $4.75 million contract with the Boston Bruins on 28 July 2021.^[33] During training and camp and the pre-season, Haula centered a line with Jake DeBrusk and Nick Foligno.^[34][35] On 13 November 2021, Haula scored his first Bruins goal, as part of a road game 5–2 Bruins win against the New Jersey Devils.^[36] Despite a slow start, Haula would finish the season with 18 goals and 44 points in 78 games, his best totals since 2017-18.

New Jersey Devils

On 13 July 2022, Haula was traded to the New Jersey Devils in exchange for Pavel Zacha.^[37]

On 23 June 2023, he signed a three-year, $9.45 million extension with the Devils.^[38]