Baker scored on Starlin Castro's fly to end game that lasted 6 hours, 27 minute, a record for longest game by time for both teams.
Chicago used seven relievers before Baker (1-0) became the first Cubs position player to take the mound since Aug. 27, 2012, when Joe Mather faced Milwaukee.
The Rockies also used all seven relievers in their bullpen, then turned to Tyler Matzek, a starter in the 16th.
Matzek (2-5) walked Baker to lead off the inning. Baker advanced to second on a sacrifice, then third on Anthony Rizzo's bloop single before scoring.
