42 is the Answer.

Here is a list of every Red Sox pitcher who compiled 20 or more saves from 1997 through 2013.
- Jonathan Papelbon (219)
- Derek Lowe (85)
- Tom Gordon (68)
- Ugueth Urbina (49)
- Heathcliff Slocumb (48)
- Keith Foulke (47)
- Mike Timlin (27)
- Alfredo Aceves (27)
- Tim Wakefield (22)
- Koji Uehara (21)

Note that this list excludes several would-be closers who failed to get to 20 saves:
- Joel Hanrahan (4)
- Andrew Bailey (14)
- Mark Melancon (1)
- Daniel Bard (5)
- Curt Schilling (9)
- Rod Beck (6)
- Butch Henry (6)
- John "Way Back" Wasdin (3)
- Rich "El Guapo" Garces (5)

Here is the same list for the Yankees:
- Mariano Rivera (652)
- Rafael Soriano (44, but only because Rivera tore his ACL last year).

Happy trails, you magnificent bastard.

Seriously, spend some time on Rivera's Baseball Reference page. Look on his works, ye mighty, and despair.