Hamilton improved his average to .351 before leaving in the seventh inning with soreness in his right knee.
Nelson Cruz and Vladimir Guerrero also had three hits, and Bengie Molina homered in the six-run first inning to help the Rangers halt a four-game losing streak. Tommy Hunter (6-0) held Boston to five hits before leaving with a 7-2 lead with two outs in the seventh.
J.D. Drew and Bill Hall homered for Boston, which has lost six of its last eight games.
Tim Wakefield (3-8) had his shortest outing since September, 2008, allowing six earned runs on eight hits and striking out two before leaving three batters into the third inning.
The Red Sox had only five regular starters in the lineup because of injuries to Dustin Pedroia, Adrian Beltre, Victor Martinez and Jacoby Ellsbury. Felix Doubront has been called up from the minors to pitch on Friday because of injuries to Clay Buchholz and Josh Beckett.
The Rangers entered the game with a 4 1/2 game lead in the AL West despite being swept by lowly Baltimore in four games heading into the All-Star break. That included Hunter's worst start of the season, in which he allowed three earned runs in six innings in a no-decision.
They didn't wait long to turn things around.
After Wakefield struck out Elvis Andrus to lead off the game, he gave up six straight hits. Michael Young, Ian Kinsler and Guerrero all singled, Hamilton doubled and Cruz singled to make it 4-0. Molina hit a two-run homer before Wakefield got the bottom two in the order to end the inning.
After a 1-2-3 second inning, the Rangers put three straight batters on – one on an Hall's error at third base – to make it 7-0 and chase Wakefield. Robert Manuel inherited runners at second and third and nobody out and pitched out of the jam to avoid further damage.
Notes: The Red Sox observed a moment of silence before the game for former Yankees owner George Steinbrenner and public address announcer Bob Sheppard. … The Rangers signed OF Josh Richmond, a 12th-round pick from the University of Louisville, and assigned him to Spokane of the Northwest League. … Wakefield is 2-6 with a 6.75 ERA in nine starts since May 28. … Hall made a diving catch on Molina in the fifth to deprive him of extra bases down the line. … Texas, which stole nine bases against Wakefield on April 20, stole one on Thursday to extend their streak to 35 in a row without being thrown out. Cruz was caught trying to advance to second on a pitch in the dirt that was not ruled a stolen base attempt.