At international level, Giusti played a part in five major tournaments for Argentina. 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. Argentina were defeated 1–0 by West Germany in the final of the competition.