Guerrero celebrated his return with a two-run homer, his 16th of the season, in the seventh against Kevin Jepsen.
But the Angels prevailed when Fernando Rodney left the bases loaded in the eighth, thanks largely to a brilliant play by center fielder Torii Hunter, and Brian Fuentes worked a perfect ninth for his 14th save. One of Fuentes' two strikeout victims was Guerrero.
Texas' division lead was trimmed to 3 1/2 games.
"They're playing great baseball," Angels manager Mike Scioscia said, "and you have to play well in a lot of areas to beat them."
Oliver spent three years supplying leadership and outs in the Angels' bullpen, but he's on the other side now along with Guerrero and another ex-Angel, reliever Darren O'Day.
"Every-day Darren Oliver," said Hunter, who used his Gold Glove defense to snag Julio Borbon's drive to deep right center with two on and one out behind Rodney. "He's pitching every day and knows what he's doing. But Bobby got a pitch up and was able to capitalize."
Oliver came in with eight consecutive scoreless appearances, retiring 25 of 27 hitters. But he walked Howard Kendrick on four pitches to load the bases in relief of Scott Feldman, and Abreu worked the count full before driving a ball into the right-field corner.
"I threw a curveball 3-2 and it kind of hung a little bit," Oliver said. "He did what he's supposed to do with it. He's tough, man. You really have to make your pitches with him."
A 2-2 cut fastball was close, Abreu acknowledged, but the call went his way, and he turned Oliver's strike into a rocket.
"I took that one cutter, and I thought, `Oh, very close,' " Abreu said. "It could go both ways, and I'm glad it went my way. The pitch I hit was a breaking ball that stayed around the middle.
"We have to score some runs. When we do that, our pitchers are more comfortable. Pineiro always keeps us in the game, and Fuentes did a really good job closing it out against their 3-4-5 hitters -- especially with Vladdy as hot as he is."
Three times Texas took the lead against Pineiro, and each time the Angels came back to tie it against Feldman.
The rally in the sixth came with two outs. Kevin Frandsen singled and scored on Jeff Mathis' shot past shortstop Elvis Andrus after a wild pitch. Erick Aybar singled, Oliver was summoned, and Abreu delivered.
Pineiro, extending his winning streak to five games and moving to 8-6, had yielded just three earned runs in his previous 24 1/3 innings.
The Rangers had a chance to break it wide open in the fifth. But Pineiro exercised damage control by holding Texas to one run after they had loaded the bases with nobody out and the heart of the order on tap.
"That was the biggest turnaround in the game there," Pineiro said. "We got out of that inning with one run, and I trusted this offense to do what they do.
"My main thing there was keeping the ball down. No outs, bases loaded, I told myself to look for ground balls. That was huge."
Guerrero grounded into a force at home for the first out, a takeout slide by Andrus preventing Mathis from throwing to first.
Josh Hamilton, who had earlier extended his hitting streak to 22 games, produced a run with another force-out on a grounder snatched by Mike Napoli at first for the lead.
When Nelson Cruz flied out to end the inning, Pineiro had kept the Angels in the game.
It all started with a bang. Ian Kinsler, the third man to face Pineiro, homered to left center.
Aybar's legs got the Angels even in the bottom half of the first when he came all the way around from first to score on Kendrick's single down the right-field line. Aybar crashed into Texas catcher Matt Treanor while scoring but was uninjured.
Guerrero's sacrifice fly had the Rangers back in front in the third, and Napoli tied it with his team-high 14th homer to left in the fourth inning.
Guerrero capped his big night with his two-run shot to dead center on a 94-mph heater thrown by Jepsen with two outs in the seventh.
"It was Vlad," Rangers manager Ron Washington said. "He got us a two-runner straight to center field against Jepsen with two strikes. It put us within one run, and the next three innings we fought pretty good and had opportunities but just didn't deliver."
Hunter had a big hand in that, outrunning Borbon's treacherous drive.
"I said, `Come on legs, don't fail me now,' " Hunter said. "When you see a ball like that, all you think about is going and getting it."
Reaching home plate in the first inning, Guerrero lifted his cap to the roaring crowd in appreciation.
"It was a very nice moment," Washington said. "I thought they treated him with a great deal of respect. He's done great things with the Anaheim Angels and they showed him respect. I got chills."