Hamilton set an American League record with 18 total bases. He hit two-run homers in the first, third, seventh and eighth innings, scoring Elvis Andrus ahead of him each time.
It was the 16th four-homer game in major league history. Hamilton became the first AL player ever to go 5-for-5 with four homers in a single contest.
Adrian Beltre also went deep for the Rangers, who have won two straight against the Orioles by a combined score of 24-6.
Neftali Feliz (2-1) earned the victory, yielding one run on four hits over six innings while walking two and striking out eight.
Orioles starter Jake Arrieta (2-3) surrendered three of Hamilton's blasts, accounting for all six of his runs allowed on nine hits over 6 1/3 frames.
Nick Markakis went 3-for-5 with a solo home run and two RBI while J.J. Hardy also homered for Baltimore.