Selected by the Twins in the second round of the 1978 draft, Jesse was used the following year in a deal to bring veteran southpaw Jerry Koosman to Minnesota. Jesse saw little action in the bushes as the Mets gave him a lengthy look in 1979. He spent 1980 and ’81 back on the farm with a brief trial at the end of the ’81 season. He was up for good by 1982, the year he established himself as a reliable fireman. That year he led the Mets bullpen with a 2.72 ERA.
Orosco had his best year in 1983 when he won 13 games, saved 17 games and fashioned a 1.47 ERA in 110 innings of work. The southpaw fireman kept batters off-balance, limiting batters to an average of just 0.691 hits per inning. The Mets made Jesse their regular closer in 1984 and he responded by saving 31 games. In 1985, the Mets brought up Roger McDowell, and Jesse and Roger each nailed down 17 saves.
The Mets went to the World Series in 1986 as Orosco saved 21 games during the regular season on a nifty 2.33 ERA. In his first postseason action, Jesse won three games in a classic NLCS showdown with the Houston Astros of Mike Scott and Nolan Ryan. Jesse kept his fine pitching up in the World Series against the Red Sox by posting a 0.00 ERA and saving a pair of games.
When his ERA climbed in ’87, Jesse, who averaged a strikeout per inning, was involved in a three team trade that sent him to the Dodgers. In California, Jesse trimmed his ERA back down to a more Orosco-like 2.72. In his one year with the Dodgers, Jesse was a member of a strong bullpen that boasted the talents of Jay Howell, Alejandro Pena, Tim Crews and Brian Holton. Granted free agency after the season, Jesse ventured to the American League, signing with the Indians of Cleveland.
Jesse owned American League batters with a 2.08 ERA and an average of one strikeout per inning of work. With the Brewers bullpen in 1993, Jesse had one of his finest strikeout seasons when he fanned 67 batters in just 57 innings. He joined the Orioles via free agency in 1995 and led the American League with 65 games pitched. He pitched in 66 games in ’96 and appeared in 71 contests in 1997, when Baltimore made it to the postseason. As a 40-year-old in ’97, Jesse tossed 2.2 scoreless innings in the Playoffs.
After he struggled in ’99, it appeared that the 42-year-old Orosco was done, but he caught on with the Dodgers in 2001 and enjoyed a strong season as a left-handed specialist. He appeared in 56 games in 2002 and fashioned a 3.00 ERA. In his last Major League season, 2003, Jesse pitched for three different clubs. Orosco holds the record for most games pitched with 1,252.
W 87/L 80/PCT .521/SV 144/G 1,252/IP 1,295/H 1,055/BB 581/SO 1,179/ERA 3.16