Born at Vicenza, Bordin made his first breakthrough at the 1986 European Championships, where he won a gold medal. His next international competition was at the 1987 World Championships in Rome. The marathon race was held on a very hot and humid day, and Bordin wisely held back from the leaders in the early stages. He caught up the leaders after the 35 km mark and finally settled to third place.
At the Olympic marathon in Seoul, Bordin stayed with the leaders from the start, and after 25 km (16 mi) the leading pack started losing contact one by one, and with 5 km (3.1 mi) remaining, only three runners remained: Bordin, Douglas Wakiihuri from Kenya and Hussein Ahmed Salah from Djibouti. With 3 km (1.9 mi) to go, Salah and Wakiihuri sprinted forward, and Bordin passed them with 1 km (0.62 mi) to go to win the gold medal.
Bordin successfully defended his European marathon title in 1990, becoming the first man to win the title twice, but at the 1991 World Championships in Tokyo, he finished in a disappointing eighth place. Bordin attempted to defend his Olympic title at 1992 Summer Olympics in Barcelona, but he strained a groin muscle jumping over a fallen runner just after the halfway mark, and failed to finish. Shortly after the Olympics Bordin decided to retire.
Bordin is the only male to win both the Boston Marathon and an Olympic gold medal in the marathon. He won the Boston Marathon in 1990 and describes the victory as his "second greatest run, after winning the Olympics".