Innis pitched in only 12 games in 1988 before being sent down to the minor leagues. However, he posted a career-best 1.89 ERA in the majors that year, and was credited with his first major league win on June 4 against the Chicago Cubs. He started the 1989 season with the Tidewater Tides and remained there until June, when Terry Leach was traded to the Kansas City Royals. Innis finished the year with a 3.18 ERA and 16 strikeouts over innings. He was limited to three games pitched in April of the following year before being sent back to Tidewater. He was eventually promoted back to the major league roster in June and collected his first major league save on June 29 against the Cincinnati Reds. During the 1991 season, he compiled a 0–2 win–loss record along with a 2.66 ERA and a career-high 47 strikeouts in innings. He finished ninth in the National League (NL) in games pitched (69), and became the first major league pitcher to appear in 60 games without recording a win or a save. This ironically factored against him during salary arbitration at the end of the season. Innis had a 6–9 record, a 2.86 ERA and 39 strikeouts in a career-high 88 innings pitched in 1992. He set a franchise record of 76 games pitched, and finished fifth in the league in games pitched and sixth in hit by pitch (6).
