The Rangers are now one game ahead of the Red Sox in the American League Wild Card race and 4 1/2 behind the Angels, who also won Monday.
"We're playing baseball," manager Ron Washington said. "They can't go out and hit the ball out of the ballpark all the time. Sometimes you've got to take advantage of what you got. Maybe we didn't get anything to drive."
The Texas offense scored on a barrage of early hits off Minnesota starter Francisco Liriano, who gave up seven runs over two innings and was sent to the disabled list with a tired arm after the game.
Center fielder Marlon Byrd earned an RBI the hard way after a pitch that bounced in the dirt and nicked him with the bases loaded. David Murphy then singled a runner home and, two batters later, Hank Blalock hit a sacrifice fly which gave the Rangers a 3-1 lead.
With one out in the second inning, the first three hitters in the Rangers' lineup reached base once again. Byrd provided a two-run single, which Murphy followed with a sacrifice fly. Andruw Jones followed with a single to give the Rangers a 7-2 lead.
"We're trying to become a more versatile offense," third baseman Michael Young said. "We did a good job taking walks and finding a way to get on base."
The first four batters in the Texas lineup -- Ian Kinsler, Young, Josh Hamilton and Byrd -- went 7-for-15 (.467) with two doubles, three RBIs, three walks and seven runs scored.
Young now has hit safely in 19 consecutive home games and has batted .386 (27-for-70) over that span.
Every starter had a hit except Blalock. Catcher Kevin Richardson, making his Major League debut, had two, including a single to center field for the first of his career.
"Anytime you can get the first out of the way is good," Richardson said. "It was just a hit up the middle. As soon as it got past the pitcher, I knew it was going through. It was just a special feeling."
Richardson became the second catcher in Rangers history to collect multiple hits in his Major League debut. The other was Chad Kreuter on Sept. 14, 1988, against the Athletics.
Tommy Hunter didn't have an especially strong outing for the Rangers. He gave up four earned runs over 5 2/3 innings pitched with three walks and four hits allowed.
"The first two innings, Tommy was having trouble," Washington said. "Tommy was scattering his fastball a little bit, couldn't get on a changeup. He was trying to find a pitch he could get over the plate. But from there, he started to fight like the warrior he is."
Hunter said his first and second innings were difficult as he battled some early wildness. He settled down after allowing runs in each of the first two innings, one on a solo home run to Twins catcher Joe Mauer and another on an RBI double by Delmon Young.
"I think tonight was the best I've seen Tommy pitch," Young said. "He became a better big league pitcher tonight. Tonight was better than him going eight innings."
Hunter left with two outs and two on in the sixth inning in favor of Darren O'Day, who allowed a walk to load the bases and then another walk to plate a run before Nick Punto's two-run single, which brought the score to 7-5.
That forced Washington to pull O'Day in favor of Neftali Feliz, who induced a groundout to end the threat.
Feliz then added another perfect inning with less-than-normal velocity. His fastest pitch of the night was 97 mph.
"[Feliz] could've had the gun lighting up if he wanted," Washington said. "And he did when he needed it."
Hunter earned his third consecutive victory, improving to 6-2 on the season. Hunter, who has won six of his past seven decisions, has given the Rangers at least five innings in eight of his 10 starts this season.
With the win, Texas moved to 67-50, the club's second-best mark in a season since 1999 (68-49), and 19-11 since the All-Star break.