In 1983 Sundström won his first ATP title in Nice over Manuel Orantes and made the final of Madrid, losing to Yannick Noah who later went on to win the French Open that year.

After victory Sundström made the final of the German Open in Hamburg defeating Mats Wilander again on the way before losing a 5 set match against Juan Aguilera.

All of these matches were on clay; his opponents included the reigning French Open champion Ivan Lendl who was still playing for Czechoslovakia at the time.

Sundström turned around a 2-sets-to-love and 0–3 (0–40) deficit in the third set, and won the match in 5, which gave the Swedes the edge and they made the final against the United States.

Sundström also won his second singles match against Jimmy Arias, but Sweden had already clinched the Davis Cup by taking an unassailable 3–0 lead.