Maybe it won’t be so rare to join this list.
Let’s update it.
1997 ATLANTA BRAVES
4-1 victory against Houston Astros
2000 NEW YORK METS
4-0 victory against San Francisco Giants
2001 ARIZONA DIAMONDBACKS
2-1 victory against St. Louis Cardinals
2010 PHILADELPHIA PHLLIES
2-0 victory against Cincinnati Reds
2010 TEXAS RANGERS
5-1 victory against Tampa Bay Rays
2012 NEW YORK YANKEES
3-1 victory against Baltimore Orioles
2013 ST. LOUIS CARDINALS
6-1 victory against Pittsburgh Pirates
The 2001 Series didn’t end with Schilling on the mound getting the last out. The series ended with a walk off single by Tony Womack.
For sticklers of details, they played the Division Series in 1981 as well and two more complete games clinched series THAT year.
1981 MONTREAL EXPOS
3-0 victory against Philadelphia Phillies
1981 LOS ANGELES DODGERS
4-0 victory against Houston Astros
But while relievers were being used more frequently then, the whole specialization of EVERY bullpen role (and the cheapening of the save) didn’t come around until the late 1980s.