Seattle was debuting a rookie pitcher of their own, but Hector Noesi only managed 3 innings.
Texas, which has power up and down the line-up, had four different batters -- Josh Hamilton, Ian Kinsler, Nelson Cruz and Mitch Moreland -- go yard on Monday.
It was more than enough for Darvish, who settled down after a rough first inning, as well as the Rangers revamped bullpen. The Mariners didn't score a run after the second inning.
Alexi Ogando came on for 1.1 innings of scoreless relief, with Mike Adams handling the 8th inning and Scott Feldman, in his first appearance of the 2012 season, handling the 9th.
With the win, Texas moves to 3-1 on the year.
For more news and analysis of the Texas Rangers season so far, head over to Lone Star Ball.