Rostagno's best performance at a Grand Slam event came at the 1988 U.S. Open, where he reached the quarterfinals before being defeated by Ivan Lendl. At several other Grand Slam events, he defeated or almost defeated several tennis hall of famers. At Wimbledon in 1988, Rostagno lost a five-set third round match to Jimmy Connors, who at the time was ranked fifth in the world. At the 1989 U.S. Open, Rostagno had a match point in his second round encounter with Boris Becker, who won that point on a lucky net cord passing shot and eventually the match 1–6, 6–7, 6–3, 7–6, 6–3, en route to his lone U.S. Open title. At Wimbledon in 1990, Rostagno defeated John McEnroe in straight sets in the first round. At Wimbledon in 1991, Rostagno defeated ninth ranked Pete Sampras in four sets in the second round and Connors in straight sets in the third round.
Rostagno finished his career with a 3–2 win-loss record versus McEnroe, winning their last three matches, and a 2–3 record versus Connors, winning their last two matches. Against other top players, Rostagno was 2–1 versus Sampras, 1–0 versus Yannick Noah, 1–1 versus Mats Wilander, 2–3 versus Lendl, 1–2 versus Becker, 3–6 versus Jim Courier, 0–1 versus Michael Chang, 0–1 versus Todd Martin, 0–2 versus Andre Agassi, and 0–4 versus Stefan Edberg.