The Rangers took three out of four in the series and moved 5 1/2 games in front of Oakland at the top of the American League West. Texas has the best record in the league by five games over both the New York Yankees and Baltimore.
Kinsler then led off the 10th with a triple off Greg Holland (6-4) and scored two pitches later when Young singled to center. Texas loaded the bases later in the inning, but could not add to its lead.
Joe Nathan came on in the bottom of the 10th and Kansas City put a runner on with one out when Kinsler made a fielding error at second base.
Nathan, however, got Alcides Escobar to ground into a double play and collected his 30th save.
The win went to Mike Adams (4-3), who worked around a one-out single in the ninth.