At international level, he won the FIFA World Cup with Argentina in 1986 and was also a member of the runner-up national squad in the 1990 edition of the tournament.

During his career, Giusti played for Unión de Santa Fe, Argentinos Juniors and Newell's Old Boys, but he had most of his success with Independiente where he captained the team in their most successful era, and was part of the sides that won the Primera Division Argentina titles in the 1983 Metropolitano Championship and during the 1988–89 season.

He won the FIFA World Cup with Argentina in 1986, where he played in every game for the eventual champions.

He also played in the 1990 FIFA World Cup where, after missing the first two group matches, he went on to figure in every game up till the semi-finals where Argentina knocked out the hosts Italy.

Giusti was sent off in that match after a second bookable offence where he elbowed Italian forward Roberto Baggio.