Texas maintained a five-game lead over the Los Angeles Angels with seven games remaining in the regular season, thus reducing the Rangers' magic number for clinching the AL West crown to three.
Neftali Feliz stranded the potential tying run in scoring position in the ninth to preserve the 90th win of the season for the Rangers. It is the second year in a row Texas has reached 90 victories, but only the fifth time it has happened in the 50-year history of the franchise.
It was still a 2-1 game heading into the eighth. Kinsler led off the inning with a homer to left off Grant Balfour and Hamilton followed one out later with a blast to right.
Koji Uehara (2-3) got the win with an inning in relief of starter C.J. Wilson. Feliz issued a leadoff walk in the ninth to Josh Willingham, who eventually reached second with two away. Kurt Suzuki was then retired on a fly ball to right, giving Feliz his 29th save.
Balfour (4-2) gave up the two home runs in his only inning.