Pujols went 3 for 4 to tie 19th-century star Cap Anson for 23rd with 3,081 hits. His 633rd homer was his 16th in 59 games in Arlington.
"This is a tremendous offensive ballpark," Angels manager Mike Scioscia said. "Albert swings the bat pretty well wherever he goes."
Pujols hit a solo home run in the second inning and a two-run single in the third against Rangers starter Martin Perez.
"I threw a bad pitch to Pujols, and he hit a home run off me," Perez said.
Pujols singled home another run in the seventh against losing pitcher Eddie Butler (2-3) for a 7-6 lead.
Ohtani, a left-handed batter, then came on as a pinch hitter and homered to center field before Taylor Ward hit his first major league homer to complete the five-run inning against right-hander Butler.
"Shohei coming off the bench was a huge hit," Scioscia said.
Winning pitcher Cam Bedrosian (5-2), the second of five Angels pitchers, got two outs in the sixth.
Los Angeles took a 6-2 lead with two outs in the fourth on a three-run double by David Fletcher.
Texas came back with four runs with two outs in the bottom of the inning to tie the game against Angels starter Andrew Heaney. Odor singled home a run and the second scored as Andrus struck out but reached base on a wild pitch. Adrian Beltre drove in two runs with a bloop single.
"I was frustrated," Heaney said. "In the fourth inning, a walk to the 9-hole hitter and let it snowball from there."
With two outs and first base open, Pujols struck again in the third with his two-run single for a 3-2 lead.
"The two-out RBI, the double down the line and then the slider to Pujols in that situation where he gave up the runs," Texas manager Jeff Banister said, "it just seemed to be a lot of pitches mid-across and tight.
Angels: Before the game, manager Mike Scioscia said he hadn't seen information about RHP/DH Ohtani's bullpen session Saturday. He's scheduled for another bullpen. "His workout in Arizona will probably be more aggressive," Scioscia said.
Rangers: LHP Mike Minor (stiff back) was scratched from Friday's start, but has played catch and said, "I'll pitch in a couple days." . RHP Chi Chi Gonzalez, who underwent Tommy John surgery in July 2017, made his first appearance since 2016 on Friday night in the rookie Class Arizona League. He retired all six batters he faced, striking out two, and is expected to continue pitching in Arizona.
RAIN, RAIN GO AWAY
The game and the ceremony honoring Rangers RHP Bartolo Colon were delayed 2 hours, 26 minutes because of a downpour that began just minutes before the scheduled 7:05 CDT start. Rain fell again in the first through sixth innings. The game ended at 12:59 a.m.
"It was sloppy out there," Scioscia said. "We were a little afraid at times."
EL PRESIDENTE HONORS BIG SEXY
In a pregame ceremony, Dennis "El Presidente" Martinez recognized Colon for breaking his career record for wins by a Latin American player with Colon's 246th victory on Aug. 7.
Martinez helped Vernon Wells Sr. unveil Wells' original artwork with images of Colon in a Rangers uniform and portraits of Martinez and Juan Marichal, whose record Martinez broke in 1998. Martinez then raised Colon's hand to recognize that he was the champion.
ANDRUS TIES, SETS RECORDS
Elvis Andrus's first-inning single extended his hitting streak at Globe Life Park to 37 games, every game he has played this season, to tie Rafael Palmeiro (2003) and Michael Young (2009) for the stadium record. With a streak of 44 consecutive games since last September, Andrus broke Julio Franco's 1993 record for the longest home-game streak in franchise history.
Angels: RHP Jaime Barria (8-7, 3.50) will try to help Los Angeles gain a split of the four-game series. He's 2-0 against Texas this season with a 0.82 ERA in 11 innings.
Rangers: RHP Yovani Gallardo (7-2, 5.33) will start with RHP Bartolo Colon (7-10, 5.19) bothered by what manager Jeff Banister called "a little stiffness."
Yankees manager Aaron Boone says LHP Justus Sheffield could give the team "a couple of innings (out of the bullpen) if we needed it."
Rick Sutcliffe dissects the Yankees' recent struggles and who needs to step to make a run in the postseason.
Jose Abreu, who has 22 home runs and 78 RBIs this season, will miss the White Sox's series against the Indians due to an infection in his right thigh.
Trevor Bauer threw to hitters for the first time since breaking his right leg last month and hopes to be back on the mound for Cleveland in time for the postseason.
Mookie Betts initially said he expected to be ready for Tuesday's series opener against the Yankees, but the side injury he suffered Sunday will keep him out of the lineup.
Baseball union officials met last month with the management of the four major league teams accused of improper spending of revenue sharing money, according to The Associated Press.