Harvey, a right-handed relief pitcher, originally joined the California Angels by signing a free agent contract in 1984. He made his debut with the team in 1987, appearing in three games for the club.
In 1988, Harvey assumed the role of primary closer for the Angels, collecting 17 saves along with a 7-5 record and a 2.13 ERA.
In 1989 and 1990, Harvey continued as closer for the Angels, racking up 50 saves and striking out 160 in 129.1 innings. He was 7-7 with a 3.32 ERA over the two seasons.
Harvey picked up 46 saves in 1991, leading the American League and making his first All-Star team. He was unable to follow that up in 1992, as he spent over half the season on the disabled list. He was left unprotected by the team in the expansion draft of 1993, and the Marlins chose him with the 20th pick.
Harvey was the team's first closer, and he shut the door 45 times on the opposition in Florida's inaugural season by posting an ERA of 1.70 and a 0.841 WHIP. He made his second All-Star appearance, and his first for Florida for his efforts.
1994 saw Harvey open the season with six saves in the month of April, but he was unable to continue the pace, going on the DL for the month of May and most of June. After four appearances near the end of June, he went on the DL again for the rest of the season.
Harvey saw one final appearance with the Marlins on April 28, 1995, but after three batters faced and three runs allowed was taken out of the game. It would be his last appearance for the Florida Marlins.
Harvey spent 1996 signed to the California Angels but did not appear in any major or minor league appearances.
In 1997, Harvey played in the Atlanta Braves minor league system, going a combined 1-2 with a 4.91 ERA. He retired after the season.
Harvey played three seasons with the Fish, going 1-5 with 51 saves and a 2.50 ERA. He struck out 9.4 batters per nine innings and had a WHIP below 1.00.