From Rio Piedras, Puerto Rico, the New York Mets signed Oquendo as an amateur free agent in 1979 at age 15. He made his MLB debut with the Mets in 1983 and was traded to the Cardinals in 1985. In 1988, he made his catching debut, giving him an appearance at every position. From 1989 to 1991, he was the Cardinals' regular second baseman alongside shortstop Ozzie Smith. Oquendo's best season offensively came in 1989, when he batted .291, 28 doubles, .747 on-base plus slugging percentage (OPS) and a major-league leading 163 games played. In 1990, he produced his best season defensively, recording the fewest errors (three) for a second baseman in a season with at least 150 games played.