After the spotting the Mariners a four-run lead in the first inning, Texas chipped away, tying it on Cruz's blast in the third.
They took the lead in the next frame on a two-run shot from Mitch Moreland and a solo homer from Josh Hamilton.
Kinsler's clout in the eighth capped a 12-hit attack for the American League champs, who won for the third time in four games to start the season.
Japanese pitcher Yu Darvish (1-0), making his major league debut after signing a $60 million deal in January, earned the victory despite yielding five runs on eight hits in a 5 2/3-inning effort.
He walked four and struck out three.
Mariners starter Hector Noesi (0-1) was pounded for seven runs on six hits before being yanked after three-plus frames.
Kyle Seager drove in three runs and Ichiro Suzuki went 3-for-5 with two runs scored for Seattle.