[2] Borbón made his Major League debut on April 9, 1969, for the California Angels in a 7–3 home win over the Seattle Pilots.

He proved to be one of the most effective and durable relievers in baseball for the Big Red Machine; he was in the top five in the National League in games pitched in six consecutive seasons from 1972 to 1977.

Borbón and Carroll, along with relievers Wayne Granger, Will McEnaney, and Rawly Eastwick, anchored a bullpen that enabled Reds manager Sparky Anderson to change pitchers frequently, earning him the nickname "Captain Hook.

"[2] Of Borbón, Reds teammate Baseball Hall of Famer Tony Pérez said, "He may have been the most critical part of that great bullpen because he was such a rubber arm.

He was especially effective in the 1976 National League Championship Series, pitching 41⁄3 scoreless innings of relief in a three-game Reds' sweep.

After a bench clearing brawl, Borbon started to fight with New York Mets pitcher Buzz Capra.

[7] A year later in another brawl during the fourth inning of a 2–1 loss to the Pittsburgh Pirates in the second game of a July 14, 1974 doubleheader at Three Rivers Stadium, Borbón pinned Pirates' hurler Daryl Patterson to the turf, began pulling out clumps of his hair and bit him in the side.

Patterson lost a piece of flesh in the incident and received a precautionary tetanus shot.

[8] Borbón also bit a bouncer on the chest during an altercation at a nightclub called West Side Story in Monfort Heights, Ohio on May 4, 1979.

[2] During the Major League Baseball strike of 1994–95, Borbon was a member of the Cincinnati Reds replacement team.