On August 6, 1986 — Rangers infielder Toby Harrah hits a 2nd-inning grand slam and Larry Sheets and Jim Dwyer both go deep for grand slams in the Orioles’ nine-run 4th as Texas beats Baltimore, 13 – 11, establishing a new record for homers with the bases full in one game.

Source:
Baseball Reference August 6
National Pastime
Retro Sheet
Hall of Fame
SABR Games Project
Replay The Game