Trout became the youngest player to reach at least 275 home runs and 200 stolen bases, while Pujols' three-run drive in the eighth gave him his 17th season of 20 home runs or more.
Pujols' shot to right-center off Josh Smith helped cap a seven-run eighth inning. It is the 3,184th hit of Pujols' career, tying him with Cal Ripken Jr. for 14th all-time. It made him the fifth player with at least 17 seasons of 20 or more homers, joining Hank Aaron (20 seasons), Barry Bonds (19), Frank Robinson and Willie Mays (17).
"I've had an unbelievable career and still have another couple years left," the 39-year old first baseman said. "I just try to stay focused even through it has been challenging. Injuries happen. It hasn't been good since I left St. Louis but I work hard and don't take anything for granted."
Pujols has had a good weekend against Boston pitching with six hits and six RBI. He had his first four-hit game in two years in Friday's 15-inning loss.
Manager Brad Ausmus kept Pujols in Saturday's lineup because they were facing a lefty. Pujols was adamant that he was good to play, but Ausmus wanted to see for himself.
"I know he's going to tell me he feels great regardless. Usually I talk to guys face to face and I can tell by the body language. I guess he was right," Ausmus said.
Trout -- who was 1 for 3 with an RBI -- stole his 200th base during the second inning, becoming the first player to have at least 275 home runs and 200 stolen bases before their age-28 season. Trout turned 28 on Aug. 7, but age-season is defined by how old they are on June 30.
He is the seventh player in American League history to reach those marks -- Alex Rodriguez, Reggie Jackson, Jose Canseco, Joe Carter, Don Baylor and George Brett are the others.
Trout leads the majors with 43 homers this season and has 283 in his nine-year career.
"It's a pretty cool accomplishment. I was sitting on that one for a while, so I'm just happy I got it over with," he said.
Los Angeles trailed 4-3 going into the bottom of the eighth before blowing it open with six runs and five hits off Ryan Brasier (2-4). Andrelton Simmons' single drove in Justin Upton with the tying run before he scored on Fletcher's two-out double to left to put the Angels on top. Brian Goodwin added a two-run single with the bases loaded before Pujols' blast.
Luis Garcia (2-1) worked a scoreless eighth to get the win. The Red Sox had the bases loaded with one out but Garcia got Brock Holt to ground into a double play to get out of the inning.
"We had the matchups we liked and it just didn't happen. Brock has been clutch the whole season and he happened to hit into a double play," Boston manager Alex Cora said. "We didn't have a horrible game. We had just one bad inning."
J.D. Martinez extended his hitting streak to eight games with two hits along with two RBI. Mookie Betts added three hits.
Boston went with an opener for the first time in Cora's two seasons due to Friday's extra-inning game.
Josh Taylor worked the first inning and got out of a one out, bases-loaded jam when he struck out Justin Upton and got Calhoun to fly out to left. The right-hander allowed one hit and walked two.
Dillon Peters went 6 1/3 innings for his second-longest outing of the season. The left-hander surrendered four runs (three earned) on seven hits with strikeouts.
The Red Sox signed pitcher Jhoulys Chacin to a minor-league deal. The right-hander threw a bullpen session Friday before being signed on Saturday.
Chacin was 3-10 with a 5.79 ERA in 19 starts for Milwaukee this season before being released on Monday. Cora said he did not know if Chacin would be added when rosters are expanded on Sunday.
Angels: P Cam Bedrosian was placed on the injured list due to right forearm strain. The right-hander is the 25th player to go on the IL this season, tying the club record from last year.
Red Sox: David Price (7-5, 4.36 ERA) comes off the injured list and makes his first start since Aug. 4. The left hander missed at least four starts due to a cyst on his left wrist.
Angels: LHP Andrew Heaney (3-3, 3.95 ERA) has 24 strikeouts in his last two starts.
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Trout collects 200th career stolen base
Mike Trout becomes the first MLB player to reach 200 home runs and 200 stolen bases by his age-27 season.