Grossman hit a two-out, three-run home run capped a five-run fourth inning, and Houston beat the Texas Rangers 6-5 in 10 innings Saturday night.
The long ball comes two days after he snapped a 25 at-bat hitless skid with a two-run drive in Houston's win at Toronto.
''You have to have confidence in your ability, especially in the big leagues,'' Grossman said. ''This game is too hard not to.''
Jason Castro tripled with one out in the 10th, and Jose Altuve had a tiebreaking sacrifice fly to score the run that helped Houston end a 12-game skid against their state rival.
Marwin Gonzalez, running for Castro, scored on Altuve's fly off Rangers closer Joakim Soria (1-1).
''That was a big, big, big hit for Robbie,'' Astros manager Bo Porter said. ''He continues to swing the bat. I told him, 'It ain't going to last for long (his slump). Just keep swinging.'''
Michael Choice hit his first career homer in the ninth to tie it as Texas rallied in the eighth and the ninth to send the teams into extra innings for the second straight night.
Kevin Chapman (1-0) allowed Choice's tying homer but was the winning pitcher. Anthony Bass pitched the 10th for his second save. Texas put runners on first and third with one out in the ninth before Bass struck out Kevin Kouzmanoff and got Choice to ground out to first base.
Shin-Soo Choo came into the game having reached base 12 of his previous 16 plate appearances but struck out all five times up, including with the winning run at second base with two out in the ninth.
Houston starter Jarred Cosart shut down Texas after allowing three runs in the first four innings, limiting the Rangers to six hits while striking out a career-high eight in seven innings.
''The knock last year was the walks were too high and the strikeouts were too low,'' Cosart said. ''It's something I really worked on in spring training.''
The Rangers' streak against Houston was the longest streak in the majors between any two teams. Texas has won 18 of 21 meetings over Houston since the beginning of last season, when the state rivals became intradivision foes with the Astros moving from the National League into the American League West.
Tanner Scheppers, making his third career start since transitioning this season from short relief, was victimized by the big inning for the second time this season.
''It's a step forward,'' Rangers manager Ron Washington said. ''It's a learning experience.''
The Rangers pulled within one in the eighth when Alex Rios' double off the wall in left center scored Elvis Andrus with none out. But Rios was thrown out trying to steal third with Prince Fielder at the plate, and Texas didn't threaten again.
''Sometimes you try to make things easier,'' Rios said, ''and you make them a little harder.''
Texas scored five batters in but left two on in the opening inning. Cosart retired 10 of the last 11 batters that he faced.
NOTES: Rangers GM Jon Daniels said the club is leaning toward placing 3B Adrian Beltre on the disabled list and should decide by Monday. Beltre has been sidelined since Tuesday with a strained left quad. ... Houston called up RHP Paul Clemens from Triple-A Oklahoma City and placed RHP Scott Feldman on the bereavement list. Astros manager Bo Porter said Feldman, who pitched Friday after his father, Marshall, died Wednesday, could miss a start. ... Texas acquired RHP pitcher Hector Noesi on Saturday from Seattle for a player to be named later or cash considerations.