The left-hander struck out a career-high 10 and the Rangers capitalized on the Red Sox throwing problems for a 4-2 win Sunday.
"We didn't finish a couple of plays, and the way Wilson was pitching, that ended up being too much," Boston manager Terry Francona said.
The Rangers scored in the fourth when third baseman Adrian Beltre couldn't handle catcher Dusty Brown's throw as Nelson Cruz headed for the base. They got another run in the fifth when Julio Borbon stole home after Brown threw to second where Andrus was trying to steal.
Texas manager Ron Washington flashed a wry smile when asked if the double steal was planned.
"Elvis did a great job of stopping and allowing Julio to take off," Washington said. "He (Borbon) snuck in under the tag."
Wilson (8-5) worked 6 2-3 innings, allowing one run on three hits but walking five. He threw 113 pitches and left after walking Daniel Nava. Darren O'Day then walked pinch hitter J.D. Drew but ended the threat by getting Marco Scutaro to fly out to center.
Neftali Feliz gave up a leadoff homer in the ninth to Mike Cameron, his fourth of the year, but got his 24th save in 26 chances.
Cameron said Wilson "was kind of tough today. Strike one, strike two. Right away a couple of times I was 0-2 before I even got a chance to get in the box, so it was just a constant battle."
Wilson's last road victory came at Fenway Park in a 3-0 win on April 22. He had been 0-2 in five starts away from home since then.
"After being a closer a couple of years, I enjoy a little pressure in the ballgame," he said. "I've always enjoyed pitching here. The fans are into it. I've always enjoyed this mound."
Wilson contributed to the continuing hitting woes of the injury-depleted Red Sox, who lost for the eighth time in 11 games. Dustin Pedroia, Victor Martinez, Jacoby Ellsbury and Jason Varitek are all on the disabled list.
"It helps to have those guys in your future sight," Cameron said, "but you can't really worry about that right now."
Boston managed just five hits. In losing three of the four games in the series, the Red Sox had just 11 runs on 25 hits. Kevin Youkilis had seven of them.
The AL West leading Rangers, meanwhile, have bounced back nicely from a four-game sweep by Baltimore heading into the All-Star break.
Beltre drove in Boston's first run with a double after a single by Youkilis in the second.
Texas went ahead 2-1 in the fourth after Jon Lester (11-4) retired the first two batters and Josh Hamilton singled. Cruz doubled to left-center and Hamilton beat center fielder Cameron's throw to the plate. Cruz raced for third as the ball went home and, when third baseman Beltre bobbled Brown's throw, kept going for the tie-breaking run.
More shoddy fielding led to another Rangers run in the fifth.
With one out, Borbon doubled and took third on Andrus' infield single. Michael Young then struck out swinging and Andrus took off for second. Brown hesitated, then threw to shortstop Scutaro. As the ball sailed toward second base, Borbon sprinted home and slid in ahead of Scutaro's return throw.
"I saw he (Brown) double pumped," Borbon said. "I just tried to read it as soon as it came out of his hand. It was a big run."
It was the first steal of home by a Ranger since Ricky Ledee did it on Sept. 23, 2001, against Anaheim.
The Rangers made it 4-1 in the eighth on an even closer play when Andrus beat left fielder Darnell McDonald's throw to the plate. Andrus doubled and Young walked before Ian Kinsler singled to left. Andrus slid and his heel touched the plate at about the same time that catcher Kevin Cash's glove touched him in the chest, but plate umpire Gary Darling called Andrus safe.
Notes: Vladimir Guerrero played LF for the first time in his career, excluding two All-Star game appearances there. Hamilton, the Rangers' regular LF, filled Guerrero's usual spot as DH. Washington said he wanted to give Hamilton a bit of a rest. ... The Red Sox recalled RHP Michael Bowden from Triple-A Pawtucket and designated C Gustavo Molina for assignment. ... The game marked the 600th straight regular-season sellout at Fenway Park. Red Sox players and coaches tossed commemorative baseballs to fans before the game. The second-longest baseball streak is 455 games by the Cleveland Indians from 1995 to 2001. ... Lefties are 9 for 97 (.093) against Wilson, the worst average of any lefty starter in the majors, after David Ortiz went 0 for 3 on Sunday. ... Andrus broke an 0-for-26 slump with a single in the first and finished 3 for 4.