With two runners on and none out in the ninth, Jepsen threw a well-executed changeup to Ortiz that moved off the plate, getting Big Papi to swing and miss wildly.
''I wanted to give him a pitch he thinks he can drive, but it fades out of the zone. In that situation, I'm going for the strikeout,'' Jepsen said. ''Watching him, I've seen him come up a ton of times in that situation and tie it up.''
Jepsen then got Yoenis Cespedes to bounce into a run-scoring fielder's choice before Mike Napoli lined to center, closing out his first save since Sept. 16, 2012.
It was the fifth win in six games for the Angels, who moved a half-game ahead of idle Oakland.
''That's a great pitch,'' Angels manager Mike Scioscia said. ''It's a tough situation. David can beat you at any part of this ballpark on a variety of pitches and you've got to make your pitches there.''
Ortiz reached base four times with a double, a single and two walks for the Red Sox, who have lost three of four after winning four straight.
Boston was 1 for 14 with runners in scoring position and stranded 12 overall.
Angels starter C.J. Wilson (10-8) labored through 5 1-3 innings, giving up one run and five hits with five walks and five strikeouts.
Brandon Workman (1-7) lost his sixth straight start, giving up two runs and six hits in seven innings. He was skipped for a couple of turns to rest his arm.
''My velocity was better,'' Workman said. ''I had a chance to work on some things mechanically. I felt good tonight. I felt like I got into a nice rhythm early and was able to carry that through.''
The Angles broke ahead 2-0 on two-out doubles by Trout and Pujols in the third after Kole Calhoun walked.
Brock Holt extended his hitting streak to 12 games with an RBI single, cutting it to 2-1 in the fourth.
Los Angeles added two runs in the eighth when reliever Junichi Tazawa bobbled a grounder and made a wild throw with the bases loaded. He was charged with two errors on the play.
''Unfortunately, what looked like a potential inning-ending double play turned into a couple of runs for them,'' Boston manager John Farrell said.
The Red Sox had the bases loaded with one out in the sixth, but Dustin Pedroia bounced into a double play against reliever Mike Morin.
The most important catch of the game might have been by Scioscia. With the entire infield shifted to the right for Ortiz, Wilson had to run hard toward the Angels dugout for a short foul pop. The ball bounced in front of a hard-charging Wilson, who hopped down the dugout steps and was caught by Scioscia, with hitting coach Don Baylor assisting. ''I saw the ball, he kept coming and I said, 'No,''' Scioscia said. ''Luckily, we caught him. We don't need anybody rolling another ankle doing something like that.''
CHANGE THAT TUNE
A day after his mental gaffe cost the Red Sox in a loss to Houston, SS Xander Bogaerts changed his walk-up music to ''Rude'' by Magic!. He went 0 for 4, stranding two runners.
Scioscia said INF Grant Green, on the 15-day disabled list with a strained lower back, is ''close to playing in games.'' He'll likely need a few rehab starts before returning.
Red Sox: Pedroia was back in the lineup after missing Sunday's game because he was sick. OF-1B Allen Craig (sprained left foot) started a rehab assignment with Triple-A Pawtucket. C David Ross (plantar fasciitis) is expected to be activated Tuesday.
RHP Jered Weaver (13-7, 3.66 ERA) goes for the Angels in the second game of the series Tuesday. He took the loss against Boston on Aug. 8, giving up four runs in six innings.
RHP Allen Webster (3-1, 4.79) faces the Angels for the second time in three starts. He earned the win against Weaver recently, holding Los Angeles to two runs in 6 2-3 innings.