2009-10: Gunnarsson played in one game in AllSvenskan (Sweden's second league) as a 17-year-old while skating for Leksands' U20 and U18 teams. He also played for Vastmanland in Sweden's TV-Pucken tournament for high school-aged players. Gunnarsson had no points or penalty minutes in his only men's game with Leksands. In 14 games for third-place Leksands U20, he scored 2 goals with 3 assists and was plus-11 with six penalty minutes. In eleven games with Leksands U18, including three playoff games, he was plus-two and had 3 goals with 2 assists. In eight games for Vastmanland he had 1 goal with 5 assists and 8 penalty minutes.
2010-11: Gunnarsson played in 14 men's games – playing nine games in Allsvenskan with Leksands and five games on loan with Division 1 Falu IF – and was one of the top defensemen for Leksands U20 team. He was scoreless with no penalty minutes in five regular season games for Leksands, which finished fourth in AllSvenskan. Gunnarsson played in four of six games during the Kval playoffs and was plus-two with 2 penalty minutes. Playing for last-place Falu IF in the Division 1 C division, he had 3 assists and was an even plus/minus with 4 penalty minutes. In 38 games with Leksands U20 team he led all defensemen in points and penalty minutes; scoring 3 goals with 10 assists and finishing plus-12 with 51 penalty minutes.
2011-12: Gunnarson played for Lulea in the Elitserien as a 19-year-old rookie and gained some international experience representing Sweden at both the men's team and U20 levels. Averaging just under nine minutes of ice time in 46 regular season games with Lulea, he scored 3 goals with 4 assists and was plus-six with 8 penalty minutes. Lulea had the league's best record before being upset by AIK in the first round of the playoffs. In the five-game playoff series Gunnarsson was minus-one with no points or penalty minutes. In six games with Lulea's U20 team he scored 2 goals with 1 assist and was plus-five with 8 penalty minutes. In seven international games for Sweden, including four men's contests, he scored 1 goal with 3 assists and was plus-two but he did not play in the world championship tournaments. In his second year of eligibility for the NHL Draft, Gunnarsson was not among the 140 European skaters in Central Scouting's final rankings but was selected by Minnesota in the fifth round (128th overall).