The win improved the Rangers to 22-18 all-time on Independence Day. They are 8-2 over their last 10 games on the Fourth of July.
The win gives the Rangers their fourth consecutive victory and keeps them in a tie with the Angels atop the American League West.
"He's come a long ways," manager Ron Washington said. "His fastball is going to be something special. Tonight, he made it a point to use his off-speed stuff. He kept his fastball out of the middle of the plate. He executed."
The best example of that came in the third inning. Holland allowed a leadoff double to Dioner Navarro and a walk to B.J. Upton. He induced a fielder's choice off the bat of Carl Crawford and got Evan Longoria to ground into a double play to end the inning.
Holland ran into trouble in the fifth inning when he allowed back-to-back singles to Jason Bartlett and Gabe Kapler to lead off. Navarro hit a three-run home run that barely cleared the fence in left field and brought the Rays to 7-4.
Kapler, a former Ranger, played his first game here since May 1, 2004, when he was with Boston. This was just his ninth career game as an opponent in Arlington.
The Rangers' offense provided Holland with plenty of early cushion. Michael Young and Marlon Byrd walked with one out in the first inning before Andruw Jones hit a three-run home run to put the Rangers ahead, 3-0.
That home run was the 10th of the season for Jones, the sixth Ranger to hit that many this season. The Yankees (seven) are the only other Major League team with at least six players with 10 or more home runs.
Young added another huge hit the next inning. Taylor Teagarden led off the second with a double, which Elvis Andrus and Ian Kinsler followed with walks. Young doubled to score all three runners to push the Rangers' lead to 6-1.
It was the 300th double of his career, making him the fourth player in club history to reach that milestone. Young has posted an extra-base hit in seven of his last 17 games five multihit games in his last 12 games.
"He's a guy you pencil him in every day," Washington said. "He never quits fighting."
The Rangers offense fed off Rays' starter David Price's trouble throwing strikes early in the game.
"He just wasn't hitting the strike zone," Washington said. "We made him shrink the strike zone. When he came in the strike zone, we hit it. They couldn't leave him out there too long because he was wearing down."
Young agrees with his manager.
"We don't think we're going to score 10 every night, but we expect to have good at-bats," Young said. "We were fortunate his pitch count got up early. We did a good job of stringing good at-bats together and pushing runs across the plate."
Nelson Cruz hit a solo home run in the fifth inning. David Murphy followed that with a triple and scored on a single by Teagarden to push the Rangers' lead to 9-4.
Teagarden also drove Cruz in with a sacrifice fly in the third inning. He is hitting .459 (9-for-21) with runners in scoring position this season.
Hank Blalock and Cruz provided back-to-back RBI singles for the Rangers' final two runs of the game.