Seager drove a 1-1 fastball from José Quijada (0-5) deep to left center for his 32nd homer, extending his career-best in his first season with Texas. Quijada came in to bat the eighth and led batsman Marcus Semien on foot before Seager connected for his shot into opposite field.
Matt Moore (5-2) made three outs for the win, and Jose Leclerc handled the ninth for his seventh save on eight occasions.
Angels star Shohei Ohtani was kept out of the starting lineup, but he pinched with an out in the ninth and doubled into the right field corner. Luis Rengifo and Mike Trout then struck with verve.
Rangers won a series for the first time since August 19-22. They also took the season series from Los Angeles and were a half-game ahead of the Angels in the contention for third place in the AL West.
“Coming out and winning a series against an in-division team is something to be proud of,” Seager said.
Seager, 28, signed a 10-year, $325 million deal with Texas in December. But Rangers (65-84) are playing a sixth consecutive losing season.
Seager reached the postseason in his first seven seasons with the Los Angeles Dodgers.
“Failure always drives you,” Seager said. “You never want to lose. You remember how it feels and it makes you want to go to work in the off-season.”
Angels interim manager Phil Nevin did not blame Seager’s homer for the loss.
“We ran three leadoff hitters today and all three scored,” Nevin said. “We have to get better at that.”
Angels right-hander Michael Lorenzen was charged with three runs and two hits in more than five innings. He struck seven and walked two.
The Angels led 3-1 before Rangers rallied in game six. Leody Taveras left and Semien singled before Lorenzen was replaced by Aaron Loup.
After Seager crashed into a forceout, Nathaniel Lowe and Adolis Garcia hit back-to-back RBI singles. Jonah Heim followed up with another base hit, but left fielder Jo Adell knocked Lowe down at the plate.
Los Angeles scored three times against Martín Pérez in the third game. Trout, serving as the designated hitter with Ohtani out of the lineup, hit a two-run double with two outs and hit Taylor Ward’s single on the right.
Pérez allowed five hits, hit out five and walked three in six innings. The left-hander has won each of his two starts so far.
Ohtani did not start this season for the ninth time in 151 games. It was the first time since September 4th.
“We like to think that he’s Superman and can do it every day and stuff, but he’s human,” Nevin said. “We have to give him days off from time to time. I like to do this either the day before or after the pitch.”
Nevin said other factors include the left-left matchup against Perez and bringing Trout off the turf for a day.
Before the game, some Angels players sat quietly in the clubhouse watching a documentary about Hall of Famer pitcher Nolan Ryan, who spent nine seasons with the Angels and five with the Rangers. In it, Ryan said he assumed the December 1971 trade from the New York Mets to “sunny California” sent him to the Dodgers. Upon learning that he had been sold to the angels, he said, “I could have died.”
And the room erupted in laughter.
Angels: Ohtani (13-8, 2.43 ERA) pitches against Minnesota on Friday. He’s 3-0 in his last four starts with a .67 ERA and 29 strikeouts.
Rangers: RHP Jon Gray (7-7, 3.80 ERA) will face Cleveland’s RHP Cody Morris (0-2, 2.30 ERA) in the opener of a three-game home series on Friday night.