Dee ihe ga-aga n'ihu maka paragraf a - Ndị Cleveland Indians bịanyere aka na Murray dị ka onye nweere onwe ya na Disemba 2, 1993. N'oge 1994, ọ gbara bọọlụ na egwuregwu 108 ma nwee batting nkezi nke.254 tinyere 76 RBIs, 17 home runs na 110 hits tupu oge ahụ dị mkpụmkpụ n'ihi nkwụsị ahụ. N'afọ sochirinụ, ọ gbara bọọlụ na egwuregwu 113 ebe o nwere batting nkezi nke.323 maka 82 RBIs, 21 home runs, na 141 hits. Murray ruru 3,000-hit plateau dị ka onye India na June 30, 1995, na Hubert H. Humphrey Metrodome na otu aka nri aka nri nke Minnesota Twins pitcher Mike Trombley. Na 1995 American League Division Series, ọ kụrụ 5-maka-13 maka.385 batting nkezi mgbe ọ na-enwe otu ụlọ na 3 RBIs ka ha kpochapụrụ Boston Red Sox na egwuregwu atọ. Na 1995 American League Championship Series
, ọ gbara bọọlụ 6-for-24 mgbe ọ na-agba ọsọ n'ụlọ na 3 RBIs ka ndị Indians meriri ndị Seattle Mariners ịga n'ihu na 1995 World Series. N'usoro egwuregwu ahụ, ọ kụrụ 2-for-19 maka nkezi batting nke.105. Otu n'ime ihe ọ kụrụ bụ otu n'ime ala nke 11th inning nke Egwuregwu 3 nke Alejandro Peña iji nweta Álvaro Espinoza ma nye ndị India mmeri dị mkpa. O nwere RBIs abụọ ndị ọzọ tinyere ịgba ọsọ n'ụlọ na egwuregwu nke abụọ nke gbara ọsọ abụọ. Agbanyeghị, ndị Indians meriri ndị Atlanta Braves na egwuregwu isii. Oge Murray n'afọ 1996 bụ nke abụọ n'etiti ndị otu abụọ, ndị India na Orioles. Ọ gbara ngụkọta nke egwuregwu 152, na-akụ maka.260 na 79 RBIs, 22 home runs tinyere 147 hits. Ọ gbara egwuregwu 88 maka ndị Indians, na-akụ maka.262 tinyere 45 RBIs, 12 home runs na 88 hits. Ndị Indians gbanwere Murray laghachi na Baltimore na July 21, 1996, maka ite Kent Mercker.