Lately, he's shown that he's pretty good on offense, too.
The Astros trailed by one in the fourth inning before Dominguez launched his fourth homer of the season in left field to give Houston a 6-4 lead.
"I'm trying to figure some things out and be more consistent," said Dominguez, who is batting .239. "I've been able to get some big hits, and hopefully, the average will be there by the end of the year. But most importantly, I'll get the RBIs and get the (wins)."
Dominguez has hit all of his homers in the past nine games and his 21 RBIs are second on the team.
"This guy is growing up right before our eyes," Houston manager Bo Porter said of the 24-year-old. "He's getting more and more confidence ... I think he's gotten to the point where he understands himself, he understands what the league is trying to do to him, and now he's picking his spots and you see that he has some power."
Castro's homer came in Houston's two-run third inning before Kansas City took the lead on a three-run home run by Miguel Tejada in the fourth. It was his first homer since 2011.
Houston's Dallas Keuchel (1-1) allowed nine hits and four runs while striking out six in 6 2/3 innings for the win. He was helped by three double plays turned by his defense, which lead the majors with 60. Closer Jose Veras struck out two in a perfect ninth for his seventh save.
"Keuchel did a great job of, one, attacking the zone and being very efficient with his pitches and did a good job of pitching to both sides of the plate and using his off-speed stuff to induce ground ball double plays," Porter said.
Kansas City starter Jeremy Guthrie (5-2) allowed eight hits and a season-high six runs in five innings -- his shortest start of the season. He had gone 18 games without a loss before allowing 19 hits and 11 runs in the past two games to lose two straight.
"I never really got into a groove, and it's my own fault," Guthrie said. "Whether it was a walk or falling behind guys, I just wasn't able to put anybody away. For the most part, none of my pitches were super well-executed, and they just made me pay."
Francoeur, who entered the game in a 0 for 11 slump, had a season-high three hits for his first multi-hit game since April 30.
The Royals mustered a little more offense on Monday that they had in a weekend sweep by the Athletics when they managed just five runs in three games. But their losing streak stretched to four games after going 3 of 10 with runners in scoring position on Monday.
Royals catcher Salvador Perez was shaken up when he crashed hip-first into the railing near Houston's dugout chasing a foul ball in the fifth inning. He finished the inning, but was replaced by George Kottaras for the sixth inning. Manager Ned Yost said he has a bruised right hip and is listed as day to day.
Kansas City's three-run fourth inning ended a 36-inning streak where the Royals didn't score more than one run in a frame. Perez singled to start the inning before a one-out single by Francoeur set the table for Tejada's shot, which landed in the back of the Crawford Boxes in left field and gave Kansas City a 4-3 lead.
It was the first home run for the 38-year-old Tejada, who didn't play in the majors last season, since July 16, 2011.
"Right now, for me, even if I get a hit, it's great," Tejada said. "When I get an opportunity, I just want to help my team win a game. I'm excited to hit a home run, but I'm just trying to do my best to help us win."
Carlos Pena walked and Paredes singled in the fourth before the homer by Dominguez put Houston up 6-4.
Marwin Gonzalez led off Houston's third with a single and advanced to second on a sacrifice bunt. Gonzalez took third on an error by Elliot Johnson when he missed the catch on a pickoff try. A sacrifice fly by Jose Altuve gave Houston a 2-1 lead.
Castro's fourth homer of the season pushed Houston's advantage to 3-1.
Hosmer and Francoeur hit consecutive one-out singles in the second inning before Johnson's RBI single with two outs put Kansas City up 1-0.
Carter walked with one out in the second and Pena followed with a double to the corner of right field. The Astros tied it at 1-all when Carter scored on a groundout by Paredes.
Hosmer, the first baseman, made a nifty catch to end the seventh inning. He jumped high into the air and extended his glove to snag a liner by Paredes. He fell backward to the ground and glanced at his glove as if to double check that he actually made the catch.
The series continues on Tuesday when Houston's Bud Norris, who had his start pushed back two days after leaving his last outing because of lower back spasms, opposes Wade Davis. ... Houston OF Justin Maxwell, on the disabled list with a broken bone in his left hand, got the OK from his doctor to remove his brace on Saturday and took swings at underhand soft tosses on Monday. He said his hand is still sore but he's feeling much better. He isn't sure when he'll be ready for a rehabilitation assignment, but when he does go he'll wear a batting glove with hard plastic on the side to protect the bone he broke. ... New Astros president Reid Ryan, son of Hall of Fame pitcher Nolan Ryan, said Monday that he'd like Houston's Double-A affiliate Corpus Christi to play an exhibition game at Minute Maid Park in the future.