Alfonseca signed an amateur free agent contract with the Montreal Expos in 1989. The Marlins acquired him in the 1993 minor league expansion draft. He would not make his first Major League appearance until 1997.
Affectionately known as "The Octopus," Alfonseca has an extra digit on each hand and foot. The right handed pitcher was used exclusively as a reliever with the Marlins, and was their primary closer from 1999 through 2001.
In his first season, Alfonseca posted a 1-3 record with a 4.91 ERA, a 1.792 WHIP, and 12.6 hits allowed per nine innings pitched. He allowed opponents to hit .324 in 25.2 innings.
1998 saw Alfonseca take on a larger role, as a middle reliever and setup man for the Marlins, he managed to save eight games. He finished the season with a 4-6 record and slightly improved statistics, a 4.08 ERA, a 1.528 WHIP and 9.6 hits allowed per nine innings.
In 1999, Alfonseca took on the role of primary closer for Florida, saving 21 games and finishing with a 4-5 record and a progressive career best of 3.24 ERA.
In 2000, Alfonseca led the NL with 45 saves, posting a 5-6 record with a 4.24 ERA. He was honored with the NL Rolaids Relief award.
2001 marked the first season in which Alfonseca did not finish with a losing record. He finished with a 4-4 record and another career best in ERA, at 3.06.
He is second on the Marlin's all-time save list, with 102. He compiled a 19-25 record with a 3.86 ERA for Florida in 307 games.