Oswalt (2-0) went six innings, giving up five runs and a career-high 13 hits with two walks and six strikeouts.
"It was just one of those nights where everything comes together," Murphy said. "It was just impressive the way we showed an offensive effort from top to bottom. It was very complete."
Closer Joe Nathan pitched a scoreless ninth in a nonsave situation for the Rangers, who needed just about every run for their sixth consecutive series victory, matching the club's longest such streak this season.
Every Ranger had a hit or scored except Hamilton, who went 0-for-4 and struck out four times. He continued a prolonged slump and is 6-for-36 (.167) in his past 10 games.
Murphy led the 16-hit parade with run-scoring hits in each of the Rangers' big scoring innings.
"It was just one of those nights where everything comes together," he said. "It was just impressive the way we showed an offensive effort from top to bottom. It was very complete."
Jhonny Peralta was 3-for-4 with a two-run double in the fifth inning for the Tigers, who twice fought back from big deficits, including scoring four runs in the eighth to make a game of it.
Doug Fister (1-5), who hasn't won on the road in six starts this season, took the loss.
"He just wasn't very sharp," Detroit manager Jim Leyland said of Fister. "We pitched bad and didn't play very well at all defensively.
"Pretty much sums it up."
Murphy's three-run homer in the second capped a four-run inning, a solo shot in the fourth started another four-run surge, and he had a run-scoring single in the three-run fifth that extended their lead to 11-5.
Murphy matched a career high he set June 11, 2008, at Kansas City. It was the fourth multihomer game of his career.
In two starts this season, Oswalt is 2-0 with a 4.43 ERA in 12 2/3 innings. He gave up nine hits but only one walk and one run in 6 2/3 innings in his debut June 16.
"My command's great, I'm throwing the ball where I want to," Oswalt said. "A few balls leaked on me a little bit during the game, but overall, for all four pitches, I felt pretty good coming out of my hand, like I can throw a strike when I want to.
"For my second start, I feel pretty close to where I want to be."
The Rangers scored four runs on four hits and an error in the second.
Murphy followed with a home run to right on an 0-2 pitch.
Hamilton struck out for the third time in the fourth inning.
"I'm not concerned about Josh," manager Ron Washington said. "Give Josh 600 at-bats, and he's going to do some damage. That's all that I look at."
His second homer of the game, which landed in the Rangers bullpen in right-center, put the Rangers up 5-2.
Kinsler followed with his homer that gave Oswalt a five-run lead.
Oswalt got Cabrera to pop out softly to first and Berry was caught in a rundown on a fielder's choice on Prince Fielder's grounder to Beltre.
Down 11-5 in the eighth, the Tigers used run-scoring hits from Jackson, Young and Avila off relievers Martin Perez and Mike Adams and an error by Kinsler to score four runs.
"We hustled hard and had good at-bats," Leyland said. "You got to play better than that, pitch better than that to have a chance here.
"This was an ugly game. You just turn the page and go on to the next stop."
Cabrera had a run-scoring single in the third and Brennan Boesch had an RBI.
Robbie Ross, who pitched a scoreless seventh, extended his scoreless streak to 16 2/3 innings over his last 11 appearances. . Rangers starter Derek Holland, on the 15-day DL, retroactive to June 6, threw 39 pitches in a rehabilitation start for Triple-A Round Rock, giving up one run and three hits, including a home run, one walk and two strikeouts over three innings. . Beltre, the leading All-Star game vote-getter among AL third basemen, is hitting .567 with three doubles, two home runs and six RBIs during his current hitting streak, which he extended to eight games with a 3-for-5 night. . The Tigers have scored a run in 143 consecutive games, dating to July 17, 2011.