Taking the mound after Sidney Ponson hurled seven scoreless innings and Damaso Marte fired a blank eighth for New York, Rivera (4-4) issued a rare five-pitch walk to Mark Teixiera opening the decisive frame.
Vladimir Guerrero poked a single to right field, moving the go-ahead run to third base before Hunter drilled a hit off the left side of the mound and into center field to bring home pinch-runner Reggie Willits with the first and only run of the game.
It was a familiar and frustrating theme for Rivera, who has allowed all but one of his eight runs this season in non-save situations, yet remains a perfect 26-for-26 when pitching with a save on the line. He, like everyone else, drew a blank when tapped for possible reasons.
"I would say it just happens," Rivera said. "I wish I could explain it. If somebody can explain that to me, because when I'm going there, it's nothing-nothing. Hopefully I can get three people out and get these guys to put something on the board."
Yankees manager Joe Girardi will not adjust his bullpen sequence, saying of Rivera,"I'm going to continue to go to him, because that's his job. Mo is the greatest closer of all time. It just didn't work tonight."
Francisco Rodriguez retired the Yankees in the home half to secure his 45th save for the Angels, who own baseball's best record and continue to enjoy a cushy lead in the American League West. The Yankees, meanwhile, have lost five of their last six and dropped 5 1/2 games back in the AL East.
"We're facing good pitching," Jason Giambi said. "Those guys are good. You've got to tip your cap -- they've pitched great, and you've got to pitch a good game to keep yourselves in the ballgame against them. They don't make that many mistakes."
Though he earned a no-decision, Ponson stuck with the Angels' Ervin Santana and matched him zero for zero through seven innings. Making his sixth start this season since joining the Yankees, Ponson turned in his best performance, shutting the Angels' potent lineup out on two hits with four walks -- though he had plenty of help from his defense, which crashed into walls all night behind him.
"They know I throw the ball over the plate and I don't strike people out," Ponson said. "I'm a contact pitcher and I work fast and keep these guys on their toes. They made plays behind me."
Bobby Abreu has earned a reputation over his two-plus years in New York for tentatively approaching the blue padding in right field, but he appeared fearless on Friday. Abreu leapt and hit the wall in the fourth inning to take a hit away from Hunter and keep a no-hitter intact.
Even after Garret Anderson broke up the bid with a single up the middle leading off the fifth, Abreu tracked down Howie Kendrick's liner while hitting the wall to record a tough out in that frame.
Ponson escaped a bases-loaded, one-out jam in the sixth by getting Chone Figgins to pop out and Cesar Izturis to fly out, and got another great catch from his defense in the seventh inning as Melky Cabrera raced back, jumped and crashed into the wall with his glove over his head to rob Anderson of an extra-base hit.
"Even though I left a couple of balls up in the zone, I had great defense behind me," Ponson said. "They know I throw a lot of sinkers, plus I threw some sliders up in the zone that were normally base hits. Melky ran down a fastball down the middle in center field and on a high changeup, Bobby jumped and caught it at the wall. My defense played really good behind me and helped me out."
Clearly, Ponson was a bit lucky -- of his 96 pitches, just 48 were strikes. But that was the extent of his fortune; the effort came on a night when Santana (12-5) was just as good, if not better.
The right-hander threw eight scoreless innings in a 118-pitch outing, splashing cold water on each and every Yankees rally. Knowing their best shot might be to get to Santana early, the Yankees opened the first inning with a walk and a single, but Santana bore down and retired the next three hitters to end the frame.
The Yankees also left two runners on the sixth inning, the last of which came on a strikeout of Giambi that prompted Santana to point to the sky and slap his right fist into his glove as he walked off the mound.
"That's as good as a pitcher has thrown against us all year," Alex Rodriguez said. "It's very frustrating, because Sidney threw an unbelievable game. Regardless of who's pitching, we're better than no runs."
After coming out of the All-Star break hotter than July with eight consecutive victories, the Yankees have lost five of their last six, including the first two contests against the Angels this weekend.
"To win games, you've got to put everything together, and we have not done that on this homestand," Girardi said.
New York will see the Angels eight times in their remaining 53 games, making them a crucial stumbling block to overcome between August and October.
"We definitely took a step back," Johnny Damon said. "We know we have to go out and win games. We've got to play much better. We've got to go out and beat these good teams. We don't get to the playoffs if we don't beat these teams."