Davis matched a career high with four hits as the Rangers wrapped up a 2-4 road trip and moved a half-game ahead of the idle Los Angeles Angels in the AL West.
With one out in the 12th, Nelson Cruz doubled to the right field gap off Esmerling Vasquez (1-2), snapping an 0-for-18 slump. One out later, Davis drove a 2-2 pitch into the right-field seats for his 14th homer.
Two pitches later, Murphy followed with a shot to the same vicinity for his fourth homer.
Eddie Guardado (1-1) pitched a scoreless 11th and Jason Jennings earned his first save in two chances despite yielding two runs in the 12th. Jennings gave up a two-out, two-run single to Miguel Montero before retiring Ryan Roberts to end the game.
Mark Reynolds hit a pair of two-run homers for the Diamondbacks, who dropped to 2-10-1 in home series this season. They haven't won a series at Chase Field since taking two of three from the Chicago Cubs April 27-29.
Reynolds' first homer came in the first inning against Scott Feldman and gave the Diamondbacks a 2-0 lead.
With Arizona down 6-4 in the eighth, Reynolds hit a 3-2 delivery from Frank Francisco an estimated 433 feet into the left field seats to tie the game.
It was the second time this season, and the sixth in his career, that Reynolds has homered twice in a game. He has 21 homers, fourth in the NL.
After spotting the Diamondbacks a 2-0 first-inning lead, Texas used two singles, two walks and two errors to rally for three runs in the third against Arizona starter Jon Garland.
Jarrod Saltalamacchia and Davis opened with singles and moved up on a bunt. After Garland walked Ian Kinsler to load the bases, Reynolds allowed a run to score on his 12th error.
Garland walked Young to force in another run, and then third baseman Augie Ojeda booted Andruw Jones' hot grounder to give Texas a 3-2 lead.
After Kinsler led off the fifth with a double, the Rangers made it 5-2 on a two-run homer to left field by Jones, his ninth.
In the first, Texas shortstop Omar Vizquel singled for his 2,678th career hit, most by a native of Venezuela. The 42-year-old Vizquel moved ahead of Hall of Fame shortstop Luis Aparicio, who played in 107 fewer games.
Notes: Arizona OF Eric Byrnes will require surgery after breaking his left hand and could miss four to eight weeks. Byrnes fractured the fifth metacarpal in his left hand when he was hit by a pitch from Feldman in the second inning. The 33-year-old Byrnes is hitting .216 with five homers and 24 RBIs in the second year of a three-year, $30-million contract. ... After consulting team doctors, Arizona RHP Brandon Webb plans to meet with three more doctors before deciding what to do about his injured right shoulder. Season-ending surgery is a possibility for the 2006 NL Cy Young Award winner, who has made one start. ... Texas OF Josh Hamilton took batting practice and said he hopes to return from abdominal surgery when the Rangers face Tampa Bay in Arlington next weekend. Manager Ron Washington said he's hoping Hamilton is back before the All-Star game.