The duo started the night with back-to-back solo homers in the first inning, leading the Astros to their fourth consecutive win. Alvarez also hit two doubles while Bregman had two RBIs and two runs.
Mauricio Dubon added a two-run double in the sixth.
J.P. France (10-5) held Boston to two runs on five hits in 5 2/3 innings for the win.
Adam Duvall hit his seventh home run in nine games for Boston, which has lost the first two of the three-game series and four of five overall.
Duvall and Alex Verdugo both had two hits.
Houston's first-inning homers came against Boston righty Brayan Bello (10-8), who had kept opponents in the yard in his previous two starts.
Bregman smacked the first over the Green Monster in left-center field, before Alvarez launched his inside Pesky's Pole in right.
The 24-year-old Bello then settled down, retiring the side 1-2-3 for two straight innings. In the fourth, a double play grounder got Bello out of a two-on, one-out threat.
Boston got on the board in the third when Justin Turner's fielder's choice plus a fielding error scored Verdugo, who singled.
The Astros took advantage of two errors in the fifth, plating an insurance run and ending Bello's night after 4 2/3 innings. He allowed three runs (two earned) on four hits and two walks. He struck out two. The run scored on Bregman's RBI single through the left side. Lefty Joe Jacques relieved Bello and stranded two Houston runners.
In the Houston sixth, after Jose Abreu's one-out single and a two-out walk to Yainer Diaz, Dubon ripped a two-run double off the wall in straightaway center.
Boston got a run back as Duvall continued his power surge with a solo shot to left, his 18th homer of the season.
In the seventh, Abreu's fielder's choice grounder scored Bregman. Boston second baseman David Hamilton made a diving stop behind the bag to save a hit on the play.
Houston's Michael Brantley played his first game of the season after undergoing right shoulder surgery last August. He went 0-for-4 while playing left field and batting sixth.
—Field Level Media