The Rangers had lost the first six meetings with the Tigers this season to drop to 3-14 against them over the last three years before Hunter (3-1) pitched Texas to its seventh victory in eight games.
Hunter allowed one run and five hits in his sixth major league start. C.J. Wilson pitched the ninth for his 11th save in 13 chances, finishing it off in a light rain.
Young, who homered leading off the eighth, has three consecutive three-hit games for the first time in his career and the fourth time in the majors this season, first in the AL.
Curtis Granderson hit his 19th career leadoff homer and had three hits for the Tigers, 4-7 since the All-Star break.
Armando Galarraga (5-9) picked up victories in his first two career starts against Texas, but did not fare as well the third time around, allowing four runs and six hits in seven innings. Galarraga was a Rangers farmhand before he was traded to Detroit in February 2008.
After giving up a one-out single to Young in the first, Galarraga retired the next 12 batters. Cruz stopped the streak with a long drive to left-center in the fifth, tying it at 1 with his 24th homer.
Texas grabbed control with three runs in the sixth. Elvis Andrus led off with a double and went to third on Young's one-out single to center. When Granderson's throw to the infield missed the cutoff man and rolled into foul territory, Andrus raced home with the go-ahead run. Hank Blalock added a two-run double later in the inning.
Granderson hit Hunter's second pitch into the right-field seats for his 20th homer of the season.
Josh Hamilton hit in the No. 7 slot for the first time in his two seasons in Texas, going 0 for 4. Hamilton is hitless in his last 15 at-bats and is in a 2-for-32 slide.
NOTES: The Rangers are almost totally over the flu bug which spread through the clubhouse last week, affecting several players and coaches. RHP Vicente Padilla, who was scratched from Wednesday's start due to flu-like symptoms, is healthy again and will return to the rotation Tuesday night. ... Texas closer Frank Francisco is recovering from pneumonia, and manager Ron Washington said he did not know when he would be activated. Francisco is over the pneumonia, but has to build up his stamina. ... Tigers pitching coach Rick Knapp was on the job after collapsing on the team's charter flight to Texas earlier in the day. Knapp was rushed to a hospital for tests after the plane arrived in Texas from Detroit. Doctors ruled out a heart attack or any other serious problem. ... Texas RHP Kevin Millwood was feeling better after leaving Sunday's game against the Royals with a strained left gluteus muscle. Millwood was optimistic he would be ready for Friday night's start against Seattle.