Using the National Pastime Almanac (best tool ever!), it's possible to determine that there were six 1-1, 1 HR seasons in the major leagues between 1901 and 2008 (the Almanac hasn't been updated to include 2009 yet, alas). They are:

The above-mentioned Felix Hernandez.

Bill Lefebvre (scrub pitcher with a 5.03 lifetime ERA) for the Red Sox in 1938.

Buster Narum (another pitcher, 14-27 lifetime) for the Orioles in 1963.

Guillermo Mota (yes!) for the Expos in 1999.

Esteban Yan for the Devil Rays in 2000.

Eddie Rogers (a middle infielder and the only non-pitcher on this list) for the Orioles in 2005.

Quirk doesn't make the list because he had two at-bats with the White Sox prior to playing for Cleveland, and thus was technically 1-3 on the season. I am unsure if any other instances like that exist: Players who hit a home run in their only at-bat with one team, but also played for another team that season. I do know that Quirk, Narum, and Yan are the only players in that time period to go 1-1 with a HR in their whole career with a team, but that's not exactly the same search.

nationalpastimealmanac.com, if you want to be able to search geeky stuff like this, too. :-)

Edited to add: After posting this, I decided to go back and search for pre-1901 instances of the same stat line. There were none, which isn't surprising when you consider they hit comparatively few home runs back then and didn't substitute as much.

Last Edited By: rjb182 01/20/10 01:18 PM. Edited 1 times.