Bregman went 3-for-5 with 5 RBIs in the 15-5 victory on Sunday at Minute Maid Park.
George Springer drew first blood for the Astros, blasting a solo home run from his leadoff spot in the bottom of the first frame. Springer added another RBI on a second-inning single before Bregman followed with his first long ball of the day.
His two-run blast traveled 384.9 feet and had an exit velocity of 104.4 mph, according to Statcast.
"I don't know if it's good luck or I demand that he hits me home runs," Bregman's mom, Jackie Bregman, told AT&T Sportsnet. "I actually asked for a grand slam, so I'm slightly disappointed right now."
Isiah Kiner-Falefa hit a solo shot for the Rangers in the top of the third inning, making the score 4-1. Carlos Correa singled in Springer and Tony Kemp in the next inning, increasing the Astros' lead to 6-1.
Kemp returned in the fourth frame with an RBI single, before Bregman added another homer. His fifth-inning bomb was a three-run shot, traveling 420 feet. Bregman's blast had an exit velocity of 102.9 mph and a launch angle of 26 degrees.
Nomar Mazara and Hunter Pence brought in two more runs for the Rangers in the sixth inning, but the Astros answered with a five spot in the bottom of the inning.
Elvis Andrus plated the final two runs of the game with a two-run homer for the Rangers in the top of the ninth frame.
Springer went 5-for-5 with five runs scored and four RBIs in the win. Correa went 3-for-4 with an RBI, a run scored and a walk for the Astros.
"I'm happy to be able to contribute to help us win," Bregman told reporters. "We had a great home stand, a lot of wins and we're moving in the right direction. I was super excited to see Springer go off today. That's what so great about this team is the other night we hit three solo homers -- 7-8-9 in the order. I'm just happy to be able to contribute and help us win games."
The Astros face the Detroit Tigers at 7:10 p.m. on Monday at Comerica Park in Detroit.