Kinsler's two-out solo shot in the fourth put the Rangers ahead for good after the Royals tied it with five runs in the top half.
Murphy's two-run blast in the fifth made it 8-5, and Adrian Beltre went deep with the bases empty in the sixth to give Texas a four-run cushion.
Mitch Moreland added a two-run homer in the seventh for Texas.
Texas starter Derek Holland (3-1) struck out nine and gave up five runs and seven hits over seven innings.
Kansas City starter Jeff Francis (0-2) was knocked around for six runs — five earned — and nine hits in four-plus innings.
At Detroit, Justin Verlander pitched seven impressive innings through a misty rain, and Ryan Raburn drove in four runs.
Verlander (2-2) allowed four hits, including two home runs by Carlos Quentin and another by Paul Konerko. He finished with eight strikeouts — including the 1,000th of his career — and no walks.
Raburn hit a two-run homer for the Tigers, who have won seven straight over the White Sox.
Chicago has lost eight of its past nine overall. Mark Buehrle (1-2) went 5 2-3 innings, allowing six runs and eight hits. He struck out five and walked two.
At Toronto, John McDonald hit a two-run homer in the bottom of the 11th inning to give the Toronto a 6-4 win over Tampa Bay.
Juan Rivera hit a one-out single in the 11th off Cesar Ramos and Adam Russell (1-1) came on to face McDonald, who homered to left.
Marc Rzepczynski (2-0) got the win as the Blue Jays handed the Rays their second straight defeat.
Toronto's Jose Bautista hit his fifth home run of the season and went 3 for 3, walked twice and scored four runs.
At Seattle, Rookie Michael Pineda threw six shutout innings for his third straight victory.
The burly right-hander gave up just three hits in his first five innings and when Pineda (3-1) faced trouble in the sixth, got Kurt Suzuki to line out to left field and a ground ball from Mark Ellis to end the threat.
Oakland has now gone 18 innings since last scoring and was shut out in consecutive games for the first time since May 2008.
Seattle got just seven hits themselves, but took advantage of seven walks allowed by the A's. Adam Kennedy scored on Jack Wilson's two-out single in the second off Oakland starter Tyson Ross (1-2), then drove home a pair in the fifth.
At Anaheim, California, Jon Lester allowed only four hits over six scoreless innings, and the Boston Red Sox overcame a shaky performance by their bullpen.
The Red Sox improved to 8-5 following a season-opening six-game losing streak, making manager Terry Francona's 52nd birthday a happy one.
Lester (2-1) struck out eight, walked two and departed with a 4-0 lead after throwing 111 pitches. Boston's starters have allowed no more than two earned runs in any of the last seven games, with a 1.19 ERA during that stretch.
Dan Haren (4-1) allowed four runs, two earned, in six innings. The right-hander struck out six and walked three en route to his first loss in 13 starts.
