Bengtsson began playing for his local team, Halmstads BK, who had just been promoted to the Allsvenskan, the highest level of football in Sweden. Although World War II was going on at the time, Sweden was neutral, though playing sports in wartime did mean that the roster had to be rotated more often than normal. Because Halmstad had just been promoted, they struggled in the Allsvenskan, and they never finished higher than 6th before being relegated in 1946. When Halmstad was relegated, Bengtsonn was transferred to Elfsborg, who had been a strong team, finishing second for three straight seasons between 1942 and 1945. The year Halmstad was relegated, however, they had faltered and finished 7th. After signing Bengtsonn, the rebounded slightly, finishing fourth in 1946-47, but they finished just one point above relegation in 1947-48, and only one place above relegation in 1948-49. Bengtsson was sold to Torino in Italy in 1949, just after the entire team had been killed in the Superga air disaster. He played for one season with the Italian club, who came in sixth that year, scoring ten goals. He went on to play for OGC Nice, with whom he won the Division 1 in 1950-51. He finished as the t-10th top goalscorer with 15 goals. He and his fellow attacker Jean Courteaux scored a total of 42 goals, which was then Nice's most prolific partnership of all time. The following season, he scored twelve goals, and though he was Nice's top scorer, and Nice won the Division 1 again, he was sold to a mid-table team in Division 2, Toulouse. In the 1952-53 season, Toulouse skyrocketed to the top of the Division 2, but Bengtsson only played slightly more than half their games: He was aging, and he was 31 at the end of the season. Toulouse was promoted to Division 1, but Bengtsson stayed in Division 2, being transferred to Stade Rennais. In his first year at Rennais, he became a star forward for the team, scoring 21 goals in 35 games. The next season, however, he floundered. He played in only half the games, and he scored a mere seven goals.
After football
Bengtsson retired in 1955. He died in 2007 at the age of 85.