"You can't give away games," Torre said. "You get beat enough times without beating yourself."
Angels manager Mike Scioscia will take a "W" any way it's presented or created.
"That was incredible," Scioscia said, having moved to 5-0 against the Dodgers this season. "I've never seen a game end quite like that."
Angels left fielder Juan Rivera shot down Russell Martin trying to get back to second for the final out before Reed Johnson could score from second on a bloop single by pinch-hitter Jamey Carroll.
Moments earlier, Matt Kemp had been erased at second when Fuentes wheeled and fired a pickoff strike to Howard Kendrick covering the bag.
"We've talked about the move he has and we still got caught with it," said Torre. "That's why we have information. You need more than ability to play with. You have to keep your head in the game. We need to think and we didn't think tonight."
Two of the three outs in the inning were handled by Kendrick, eliminating baserunners as the Dodgers were collecting them on two hits, a walk and a throwing error.
"I'll take it any way I can get it," Fuentes said of his 12th save, the win going to Joel Pineiro (7-6) on a night he too found the bases full of Dodgers but managed to frustrate them anyway.
Pineiro left four runners in scoring position in the first three innings before settling into a groove, retiring 14 in a row while the Angels were manufacturing a pair of runs against John Ely (3-5) to seize the lead in the middle innings.
"I was a little too pumped up, too much adrenaline," said Pineiro, who defeated the Dodgers for the second time in 12 days and has won four consecutive starts. "Once I settled down and got on top of my sinker, everything started working. I was pitching to contact, and great defense behind me is always the key."
After a one-out walk to Andre Ethier in the eighth ended Pineiro's night, Kevin Jepsen came on to retire Manny Ramirez on a fly ball and strike out James Loney.
It remained a one-run game heading into the ninth when shortstop Brandon Wood threw wide of first on Kemp's grounder into the hole leading off against Fuentes.
Pinch-hitter Ronnie Belliard slammed an 0-2 single to center and was replaced on the bases by Johnson. After Casey Blake struck out, Fuentes took a sign from catcher Jeff Mathis, made a quick move and nailed Kemp straying too far off second with a perfect peg to Kendrick.
Fuentes then walked Martin and yielded the bloop single to left by Carroll, who was out in front of the 0-1 fastball and dropped it in the right place, in front of the onrushing Rivera.
Johnson appeared certain to score the tying run -- so certain Fuentes already was "calculating the next hitter and what I'd have to do for damage control."
Rivera got to the ball and came up firing to second. Martin was ruled out by umpire Jim Reynolds while Johnson was about 15 feet from home plate, leaving umpire Mike DiMuro waving off the run.
"Russell can't put himself in a position like that," said Torre. "You can't make mistakes like that at this level. You've got to know the outs, you've got to know the situation, when to take a chance and when not to take a chance.
"I'm pretty sure it won't happen again. That guy's got to score to tie the game. We need to think a lot better than that."
Mathis could see that Johnson wasn't going to get there in time.
"It wasn't that close," Mathis said. "I'd gone out in front of the plate, and when Juan's throw got to second, I turned back and could see in my peripheral vision that the runner wasn't there."
The Angels manufactured the go-ahead run in the fifth, triggered by Mike Napoli's leadoff double to the opposite field. Mathis reached on shortstop Rafael Furcal's second error of the night. After Wood dropped a sacrifice bunt, Kendrick's grounder to Furcal cashed in Napoli for the lead.
Pineiro walked a tightrope in the early innings, falling behind on a third-inning run produced by Kemp with a two-out double to left-center. It cashed in Ethier, who singled in front of a Ramirez single.
Ramirez was unable to score from first as Torii Hunter played the ball off the wall and made a quick relay.
The Angels got even in the fourth. Kevin Frandsen, continuing to provide a spark with his hot bat, doubled over first base leading off and moved up on Bobby Abreu's infield out. With the infield in, Hunter hit a slow roller that Furcal bobbled. Hunter reached on the error, picking up an RBI.
"We executed some things well -- the contact play with Torii, Woody's bunt, Abreu moving Frandsen over," Scioscia said. "But the difference tonight was our pitching. Joel really did the job once he made some adjustments and got down in the zone much better.
"And then we got the pickoff at second and Juan's heads-up play, and we were fortunate to win a ballgame."