Moseley departed having yielded 10 hits and six earned runs in 4 2/3 innings, but he was spared the loss that went to Justin Speier by an offense -- led by table-setters Erick Aybar and Reggie Willits -- that was doing the same kind of damage to Boston starter Jon Lester.
"They gave us plenty of runs," Moseley said. "I've gotta go deeper in games, dude. I didn't do my job.
"It wasn't my fastball I was getting beat on -- it was offspeed stuff out over the plate. In situations where I needed to make pitches, I left pitches out over the plate, and balls got put in play where [fielders] weren't. It could have gone the other way. It's the nature of the game."
After drawing even in the fifth at 6 when Vladimir Guerrero scorched a double against reliever Julian Tavarez and scored on Gary Matthews' infield out, the Angels fell silent at the hands of Boston's new big three at the back of the bullpen.
The Red Sox seized the lead in the seventh on Dustin Pedroia's solo homer against Speier, lifting it just beyond the grasp of left fielder Garret Anderson.
"The run in the seventh was a momentum swing for them," Angels manager Mike Scioscia said. "They were able to line it up."
By that he meant Okajima, Gagne and Papelbon, whose perfect ninth ended the highly imperfect yet entertaining proceedings at four hours and two minutes. This made the concessionaires happy, matching the longest nine-inning game in stadium history, a Sept. 30, 2000 contest the Angels played with Seattle.
Okajima (0.98 ERA in 51 appearances) and Papelbon (1.99 ERA in 40 outings, with 27 saves) have been close to untouchable, and now they have Gagne between them, bringing more heat.
"They're tough," Scioscia said. "They can shorten a game as well as we can. I know our bullpen can compete with them. We just didn't get it done tonight."
Darren Oliver was flawless again with four outs of relief behind Moseley, but two runs in the eighth at the expense of Scot Shields were gift-wrapped.
A passed ball by Jeff Mathis on a strikeout put the leadoff man aboard, followed by Brandon Moss' first Major League hit, an error by Shields on a pickoff and then a wild pitch completing the trifecta of miscues.
Gagne found some resistance in the eighth with Aybar getting his third hit and Willits also reaching safely for the fourth time with a walk. But the Dodgers' former closer reached back, pumped a third strike past Chone Figgins and retired Orlando Cabrera on a popup.
"They just made pitches," said Figgins, whose two-run double to right in the fourth gave the Angels a 5-4 lead and ended Jon Lester's night (3 1/3 innings, eight hits, five earned runs). "The more you stay in ballgames, the better chance you have to win. We're trying to stay in ballgames."
The Angels, swept out of Fenway Park in three April games with a fourth rained out, were hoping to return the favor. But Boston's bats came alive, with Pedroia (three hits, three runs scored) and Mike Lowell (three doubles, a single and a walk) doing most of the heavy lifting in the absence of David Ortiz.
Big Papi got the night off, with Manny Ramirez taking the designated hitter role and doubling home two runs during the four-run fourth. It was the first of three consecutive doubles to the left-center gap, J.D. Drew and Lowell driving in runs.
It was the first time in his five starts that Moseley had given up more than four earned runs, and Angels manager Mike Scioscia said he would stick with the right-hander in the No. 5 rotation slot vacated by Bartolo Colon with his elbow injury.
"He's getting acclimated," Scioscia said of Moseley, whose start was his third in Colon's slot after opening the season with two stellar starts. "Dustin has the ability to get deep in games -- good command, good movement; he can change speeds.
"In that fourth inning, a couple of balls found gaps and a couple found holes. I don't think he pitched as bad as the linescore indicates."
Moseley brushed aside the notion that the adjustment to starting after spending most of the season in the bullpen was a factor.
"It's one pitch at a time, an inning at a time," Moseley said. "I'm not thinking about the pitch count. I feel good. I throw strikes, keep guys off-balance, can make the ball move away from lefties.
"I just have to get the job done, dude."