The victory enabled the American League West Division frontrunners to avoid a three-game sweep on their way to New York for three weekend games with the Yankees wrapping up the first half.
"I never worry about anything out of my hands," Escobar said of his exclusion from the AL All-Star squad, which includes teammates John Lackey and Rodriguez. "I wanted to pitch good tonight because we needed this one after the last two games."
After a pair of subpar performances, managing only five hits in each loss, the Angels found some offensive spark from Garret Anderson, Maicer Izturis and Jose Molina in support of Escobar, who yielded just three hits and three walks while striking out eight in seven innings.
Making a start at second base as Howie Kendrick nursed a sore left index finger, Izturis celebrated his return from the disabled list with a double and a two-run triple.
"Izzy's got a nice, short stroke that allows him to stay back and let the ball get deep on him," manager Mike Scioscia said. "That allows him to drive the ball to all fields."
Izturis' two-run triple ripped past first base from the right side and was an artful piece of hitting against southpaw Ron Mahay, who'd relieved starter Robinson Tejeda, who fell to 5-8 with the loss.
Anderson, also happy to be back after missing a total of seven weeks with a hip flexor tear, singled and scored twice in front of Izturis.
"It was a good night with my swing -- that's the swing I'm looking for," Anderson said, finding more comfort from a line drive that hooked foul in the right-field corner and a 400-foot out to left-center than his two bloop singles.
Molina ripped an RBI single to right in the fifth for a 2-1 lead, and Reggie Willits followed that with a sacrifice fly.
All-Star Vladimir Guerrero stayed in the swing of things with a pair of hits and drove in a run, his 75th, second only to the Yankees' Alex Rodriguez (80) in the Major Leagues. Gary Matthews Jr. doubled, singled and walked.
Escobar moved to 10-3 -- just four wins away from his career high established with Toronto in 1999. Escobar and Lackey (11-5) give the Angels a pair of double-figure winners at the break for the first time since 1991 when Chuck Finley and Mark Langston reached the Midsummer Classic with 12 wins apiece.
Disappointed he didn't fare better in the Final Vote for the last All-Star spot, claimed by Boston's Hideki Okajima, Escobar didn't have his customary blazing start.
Carrying a 1-0 lead created by Guerrero's RBI single in the first, Escobar yielded a leadoff double to Jerry Hairston, who scored two batters later when Michael Young singled to center.
This marked the first time this season in 16 starts that Escobar has surrendered a first-inning run, pinpointing the laser focus he's bringing into games. Hitters are batting .207 against him in the first inning, and he has 18 strikeouts against only four walks.
"For me," he said, "the first two innings are very important. I'm a slow starter at times. When I'm aggressive and pound the strike zone to get out of the first two innings, I feel good."
After Sammy Sosa hit into a double play to end the first, Escobar settled into a groove. Walks to Marlon Byrd in the second and fifth inning were the only baserunners he allowed until Ramon Vazquez tripled to right in the sixth.
Escobar, leading 5-1 at the time, retired Young on a bouncer back to the mound.
The Rangers picked up a run in the ninth when Byrd culminated a perfect night with an RBI single off K-Rod.
Scioscia once again expressed disappointment over the All-Star snubs of Escobar and shortstop Orlando Cabrera.
"You can go around the league and probably find six, seven pitchers in Kelvim's situation and six or seven position players in Orlando's situation," Scioscia said. "Eskie definitely got a lot of consideration for that club, and he's definitely an All-Star."
Escobar, preparing for a family holiday in Cancun over the All-Star break, said he won't be accepting any last-minute calls as a replacement if an AL pitcher turns up lame before the game.
"If they call me, they're going to have to find somebody else," he said. "No offense to them. I think I made a good case to be there. The guys who competed with me for the [Final Vote], I think I had better numbers."
His son, Kelvim, was with him in Texas, and they're taking another trip soon.
"We're going to Cancun for the break," Escobar said.