Grossman snapped an 0-for-28 slide with a career-high four hits as the Astros completed a three-game sweep of the Texas Rangers with an 8-4 victory over the All-Star pitcher who dominated them so many times in the past.
''The way we came into here, after losing seven in a row, for our guys to respond the way they responded in this three-game series, I'm extremely proud of them,'' manager Bo Porter said.
Grossman and rookie George Springer homered for the Astros, who moved into fourth place by a percentage point over slumping Texas.
It is the first time in their two seasons since switching leagues that the Astros have not been in fifth place in the five-team AL West after mid-April.
''When you look at where we're at today, obviously we feel like we have improved as a ballclub,'' Porter said. ''At the same time, when we get to the end of the year, we'll see where we're at. It definitely feels good to be playing good baseball right now.''
Springer also made an incredible running catch in the third inning. The center fielder leaped on the warning track, reached over his head and held onto the ball when he slammed into the wall.
Houston had 28 runs and 42 hits in the series against its in-state rival that won 17 of 19 against the Astros last season.
The Rangers lost for the 10th time in 11 games and have dropped 18 of 21 overall. At 38-53, their .418 winning percentage is the worst in the majors - just behind Arizona and Houston, both 39-54 for a .419 mark.
''It's been really tough. It's been frustrating,'' outfielder Alex Rios said. ''This is a season that I believe that we're all going to remember in a bad way.''
Dallas Keuchel (9-5), one of five candidates in Internet balloting for the final spot on the AL All-Star team, allowed four runs and eight hits over 6 2-3 innings. While it wasn't his best performance, he was happy to beat the Rangers.
''Just because they've beaten us up the last couple years,'' Keuchel said. ''They've been the big brother, of sort.''
Darvish (8-5), who had thrown 20 consecutive scoreless innings while winning his last three home starts, gave up a season-high 10 hits and six runs. He struck out eight and needed 109 pitches to get through six innings.
Against Houston at home in April, Darvish allowed one hit over eight scoreless innings. The Japanese ace also had two near no-hitters on the road against the Astros last season, one in which he retired the first 26 batters.
Carlos Corporan had a two-run double in the sixth to break a 4-all tie. An inning later, Springer hit his 19th homer, a two-run shot off reliever Jason Frasor.
Grossman's solo homer, about 329 feet into the right-field corner, made it 4-all with two outs in the fifth. He also had a double in the first inning and an RBI single in the third.
Before getting recalled this week by the Astros, Grossman had an 18-game hitting streak at Triple-A Oklahoma City. But he was hitless in a span of 28 at-bats in the majors after going 0 for 4 on Tuesday night to start his third stint with Houston this season.
Adrian Beltre extended his hitting streak to 13 games with an RBI single in the Texas first. The All-Star third baseman is batting .494 (38 for 77) in his last 20 home games, and is second in the AL at .336 overall.
Houston took a 2-1 lead in the second when Corporan hit a two-out double before Enrique Hernandez tripled and scored on a wild pitch.
''The team is in a skid, but I'm telling you, they're playing,'' Texas manager Ron Washington said. '' We're not pitching very well. ... We just don't have a sustainable offense to support what's going on right now.''
NOTES: Springer also made a running catch in the right-center gap to end the third. ... Beltre was called out on strike three in the third when he stepped out of the box but wasn't granted time. When he came to bat in the sixth, Beltre had an animated conversation with plate umpire Bill Miller.