The other two:
June 11, 1963 - Frank Malzone/Dick Stuart, 15th inning at DetroitThe Red Sox press notes list the September 25, 1985 game at Toronto, which is wrong.
September 28, 1985 - Glenn Hoffman/Dwight Evans, 10th inning at Detroit
Here is the box from the 2003 game. Jeremy Giambi was the DH -- batting 8th. Ortiz (hitting .188 at the time) pinch-hit for Giambi in the 14th.
It would be roughly another month until Ortiz got regular playing time. It's interesting to look at his game logs for that season -- he usually hit 5th.