Justin Grimm settled down after a shaky start to get the win and every member of the Texas starting lineup came up with at least one hit.
Baker hit a two-run homer in the second and Berkman gave Texas the lead for good with a three-run blast in the third.
Grimm (4-3) gave up a single run in each of the first three innings, but lasted 6 1/3 while giving up 10 hits, walking none and striking out five.
Joe Ortiz came on in the ninth for the Rangers with a six-run lead, which the Mariners promptly cut to four. That led to Joe Nathan making an appearance with two away and he recorded the final out for his 15th save in as many chances this year.
The loss went to Joe Sanders (3-5), who was touched for six runs on eight hits in five frames.