Morgan was traded to his sixth franchise in March, in a trade with the Los Angeles Dodgers for center fielder Mike Devereaux, and remained with the team from 1989 to 1991. He had his first winning season as a pro in 1991 and earned his lone All-Star selection while finishing a 14–10 record. Morgan also led the National League with four shutouts in 1990, tied with the San Diego Padres' Bruce Hurst. On July 28, he was at the losing end of Montreal Expos pitcher Dennis Martínez's perfect game, even though Morgan himself was perfect through the first five innings.