In the ski jumping season 1978/79 Heinonen achieved his best career result in an A-class jumping when he finished second behind Jim Denney in the Lahti Ski Games . On December 30, 1979, Heinonen competed in his first competition in the newly created Ski Jumping World Cup . When jumping from the large hill in Oberstdorf he reached the 63rd place. The following jumping of the Four Hills Tournament 1979/80 were just as unsuccessful. It was not until February 29, 1980 in Gstaad that he was able to win his first World Cup point when jumping from the large hill with 15th place. Also in jumping from the normal hill in Lahti a week later he won World Cup points with 12th place. At the end of the 1979/80 season he was 86th in the overall World Cup with 5 points. The following season was a lot more successful. So he was able to jump into the top 10 for the first time in jumping in Innsbruck as part of the Four Hills Tournament 1980/81 . In addition, with the 7th place he achieved the highest single placement of his career. The other World Cups were also successful. Heinonen jumped his last World Cup on February 21, 1980 in Thunder Bay . There he reached an 8th place again. At the end of the season he was in 29th place in the overall World Cup ranking.