Carter's slam in the seventh inning sailed over the limestone overhang in right field and gave Houston a 9-3 lead. Singleton lined a fastball off Glen Perkins over the right-field wall that made it 14-5 in the ninth.
Dexter Fowler and George Springer also homered for the Astros. Houston has now hit 69 homers this season, well on pace to surpass last season's total of 148, third-worst in the American League.
"It puts more strain on the opposing pitchers," Astros manager Bo Porter said. "They feel like, `I can't make a mistake here, I can't make a mistake here.' That can drain on a staff."
The only other time two Astros players hit grand slams in the same game was July 30, 1969, at New York when Denis Menke and Jimmy Wynn both hit slams in an 11-run ninth inning against the Mets.
Houston players are also sensing a different vibe now that the lineup is filled with more power.
"It's been fun. We like playing off of each other," Singleton said. "That's definitely a bonus. When one person does well, it carries over and it's contagious."
Darin Downs (1-0) got the last eight outs as the third reliever to follow starter Colin McHugh, who fanned six and allowed one run over 4-1/3 innings. He walked five and was removed after throwing 101 pitches.
Trevor Plouffe and Josh Willingham hit RBI singles as Minnesota made it 5-3 in the fifth, but couldn't get any closer before Carter and Singleton powered the game away.
Houston batted around in the fourth inning, scoring three runs after Samuel Deduno (2-4) loaded the bases with nobody out by walking two batters and hitting another.
The Astros have won seven of eight on the road and 11 of their past 15 overall as they try to snap a three-year streak of losing 100 games.
It was the third time in club history Minnesota allowed two grand slams in the same game. The last time it happened was April 22, 1988, in Cleveland.
"They got us today," Perkins said. "I think they swing hard in case they hit it, and they hit them today. Theyre not as bad as people think they are. Gotta give credit to them the way they swing the bat and pitch the ball pretty well."
The Twins also officially signed free-agent designated hitter/first-baseman Kendrys Morales on Sunday to bolster their inconsistent offense.
But if Minnesota -- now three games under .500 -- wants to remain in the playoff race, it's going to need better starting pitching.
Deduno walked four and hit two while allowing five runs in three innings on Sunday, raising his ERA to 4.45.
As a group, Minnesota's starters are 19-25 with a 4.97 ERA.
"Not a good day pitching today. Used a lot of innings out there," Twins manager Ron Gardenhire said. "We still have three games to go (before the next off day), so we'll get through it. Thats the way it is. They killed it at the end."
McHugh struck out four batters in a row during one stretch and extended his scoreless innings streak to a career-high 16-2/3 before Eduardo Nunez homered in the fourth.
Springer, named American League rookie of the month after hitting 10 home runs in May, led off the eighth by hitting his second homer in three games.
"It's nice to have other guys in the lineup who do the same thing and have more protection where guys can't just pitch around me or pitch around another guy," said Carter, who led Houston with 29 homers last season. "There's another guy behind him always. It's good for all of us."
NOTES: To make room on the roster for Morales, Minnesota released Jason Kubel, who appeared in 798 games over parts of eight seasons with the Twins but was hitting .224 this year and just .158 since April. . . . The Astros recalled LHP Rudy Owens to pitch out of the bullpen and sent Paul Clemens back to Triple-A Oklahoma City for the sixth time this season. . . . The Twins unveiled a new bronze statue on the Target Plaza before the game: team mascot T.C. Bear. . . . Jonathan Villar singled three times for Houston.