Now they'll turn to veteran Jeremy Guthrie to keep it going against the offensively challenged Astros.
The Royals seek their 15th victory in 21 meetings Wednesday night when Guthrie goes after his third win in as many starts.
Rookie Yordano Ventura threw seven solid innings for his first major league win Tuesday, and Omar Infante homered and drove in two to lift the Royals (5-7) to a 4-2 victory at Minute Maid Park.
Kansas City's starters have allowed six runs during a four-game win streak over Houston (5-9).
After he won his first five decisions in 2013 to extend his franchise record of consecutive starts without a loss to 18, Guthrie is 2-0 with a 3.55 ERA in his first two outings this season.
The right-hander gave up one run and four hits over seven innings in a 7-3 home win over Tampa Bay last Wednesday. He worked his way out of trouble in each of the first three innings, then retired his final 12 batters.
''You're going to make good pitches and they're going to hit them hard sometimes,'' Guthrie said. ''But if you make good pitches, more often you're going to get an out.''
Guthrie makes his first road start after going 6-7 with a 3.73 ERA away from Kauffman Stadium last season. In his only outing against Houston, he allowed six runs and eight hits - two homers - over five innings in a 6-5 road loss May 20.
Dallas Keuchel (1-1, 3.75) will start Wednesday after also opposing Guthrie in that contest, allowing four runs and nine hits over 6 2-3 innings to pick up the win in his only start against the Royals. Eric Hosmer went 2 for 3 off Keuchel in that meeting, while Nori Aoki is 3 for 8 in their matchups.
The left-hander hopes to build on his first victory Thursday, when he allowed one run and struck out six over seven innings in a 6-4 win at Toronto.
''He was outstanding,'' Houston manager Bo Porter said. ''He did a really good job of attacking the strike zone.''
Keuchel will face a Kansas City lineup that showed some improvement in the series opener with three doubles and a home run. The Royals had posted a .262 slugging percentage without a homer while dropping their first five road games.
Hosmer went 2 for 4 on Tuesday after he had only four hits in his first 19 at-bats away from home. Lorenzo Cain is batting a team-high .342 after posting his fourth multi-hit effort.
Guthrie has been hit hard in his last two meetings with the Astros dating to his time with Colorado, going 1-1 while giving up 11 runs and 20 hits over 12 innings. Houston, though, has scored 31 runs and batted .180 while dropping nine of 12.
Jason Castro has gone 3 for 8 when facing Guthrie, but he's off to a 7-for-39 (.179) start. Matt Dominguez is 6 for 18 over his last five games after opening 3 for 28.
Both homered off Guthrie in last year's meeting.
Prized Astros prospect George Springer says he's been told he will join the team from Triple-A Oklahoma City on Wednesday. The 24-year-old outfielder had 37 homers and 108 RBIs with 45 stolen bases combined in Double-A and Triple-A last year. He was off to a strong start in Triple-A this season, too, hitting .308 with three homers and eight RBIs.