Murray was signed as a free agent by the Cleveland Indians on December 2, 1993. In the 1994 season, he played in 108 games and had a .254 batting average along with 76 RBIs, 17 home runs and 110 hits before the season was cut short due to the strike. The following year, he played in 113 games while having a .323 batting average for 82 RBIs, 21 home runs, and 141 hits.  Murray reached the 3,000-hit plateau as an Indian on June 30, 1995 at the Hubert H. Humphrey Metrodome with a single to right field off Minnesota Twins pitcher Mike Trombley. In the 1995 American League Division Series, he hit 5-for-13 for a .385 batting average while having one home run and 3 RBIs as they swept the Boston Red Sox in three games. In the 1995 American League Championship Series, he hit 6-for-24 while having a home run and 3 RBIs as the Indians beat the Seattle Mariners to advance to the 1995 World Series. In that series, he hit 2-for-19 for a .105 batting average. One of his hits was a single in the bottom of the eleventh inning of Game 3 off of Alejandro Peña to score Álvaro Espinoza. He had two other RBIs along with a home run shot in Game 2 that scored two runs. However, the Indians lost to the Atlanta Braves in six games. Murrays 1996 season was shared between two teams, the Indians and the Orioles. He played a total of 152 games, hitting for .260 with 79 RBIs, 22 home runs along with 147 hits. He played in 88 total games for the Indians, hitting for .262 along with 45 RBIs, 12 home runs and 88 hits. The Indians traded Murray back to Baltimore on July 21, 1996 for pitcher Kent Mercker.. How many home runs total did Murray score between 1994-1996?