The Yankees trailed by five runs heading to the ninth before Mark Teixeira slugged a two-run homer off Ernesto Frieri, marking the first runs the reliever had allowed in 26 1/3 innings with the Angels.
After a walk and a pitching change, the push continued as the Yankees loaded the bases against Scott Downs, with Curtis Granderson working an eight-pitch walk to force home a run.
That brought up Rodriguez, who bashed a two-run homer in the first inning but was unable to come through with one more big knock. Flicking his wrists, Rodriguez produced just a shallow pop that died in first baseman Albert Pujols' glove.
"That's obviously one of the best hitters in the game up there, bases loaded," Jepsen said. "You don't have the luxury of pitching around him. You have to go right after him."
Given the situation, Yankees manager Joe Girardi said he liked his chances.
"You think he's going to get a big hit there," Girardi said. "He swung the bat well yesterday, swung the bat well today. Even in that last at-bat, he had some good swings."
The Yankees hit four homers in the contest -- three off Angels starter Jered Weaver -- with A-Rod, Curtis Granderson, Eric Chavez and Teixeira going deep. That is usually their recipe for success, but as Girardi noted, it is difficult to win when you give up 10 runs.
Ivan Nova was down early, serving up back-to-back first-inning home runs to Erick Aybar and Pujols, and never really seemed in command on a steamy afternoon that lent itself to the long ball.
Nova struggled to find his slider and curveball, but settled down before the Angels scored three times in the sixth, including a third homer -- Maicer Izturis' two-run shot.
"I didn't have my good stuff today. It wasn't a good day for me," said Nova, who was hit for six runs and nine hits in six-plus innings. "I couldn't throw anything but my fastball when I wanted to."
Mark Trumbo capped the Angels' scoring with a solo shot in the ninth off D.J. Mitchell, the Halos' fourth blast of the day.
Granderson tried to keep the Yankees in the game, but even one of his finer days of the season wasn't enough to propel New York to a series sweep. He homered off Weaver and made two terrific catches in center field to take away extra-base hits.
The best grab of the day may have come in the third inning, as Granderson raced toward the center-field wall and snatched Mike Trout's deep drive an instant before crashing into the padded wall.
"This wall in particular is probably the hardest one in all of baseball, because it's all concrete behind it," Granderson said. "Even the padding's hard out there, so you've got to be careful going into it."
In the sixth, Granderson made a sprawling grab in the right-center-field gap to take extra bases away from Alberto Callaspo, who settled instead for a sacrifice fly.
"The good thing about days like today, when it's so dense and humid out there, the ball kind of hangs up a little bit. It helps you get underneath it," Granderson said.
The Angels shoved back with three eighth-inning runs, as Bobby Wilson and Trout connected off an ineffective Chad Qualls for run-scoring hits, and Aybar dropped a squeeze bunt on Boone Logan.
"He just missed some spots," Girardi said of Qualls. "He's a sinkerballer and he's just trying to keep the ball down, and he did a decent job of that. But he just missed some spots."
Weaver allowed five runs and 10 hits over seven innings. Rodriguez's first-inning blast snapped a personal 49 at-bat homerless stretch, but the Yankees turned in some uncharacteristically wacky adventures on the bases.
Derek Jeter punched home New York's third run with a second-inning RBI single, but was caught wandering off first base. In the third inning, A-Rod and Robinson Cano were both tagged out on the same play. Cano was picked off by Weaver and Rodriguez was gunned down trying to score.
"We had some bad reads," Girardi said. "That's going to happen. It's guys being aggressive. I don't mind them being aggressive, but sometimes they're going to make mistakes. That's the human part of the game."