Gunnarsson was in 1979 in the final of the junior tournament of the US Open , in which he lost to Scott Davis . In the same year he suffered a knee injury while training with Björn Borg , after which he always competed with a knee brace. In 1982 he became national Swedish indoor champion and he won his first double title on the ATP World Tour in Stockholm . In 1985 he was able to win the only single title of his career in Vienna , another four times in his career he was in a single final. He won nine doubles titles and stood in ten other doubles finals. He reached his highest ranking in the ATP world rankings in 1985 with position 25 in singles and 1984 with position 20 in doubles.
Gunnarsson completed one game in singles and four doubles for the Swedish Davis Cup team between 1985 and 1990 . His greatest success with the team was the final in 1989. In the 3-2 defeat against Germany , he lost at the side of Anders Järryd in five sets against Boris Becker and Eric Jelen .