Alex Gordon snapped the tie with an RBI single and Eric Hosmer added another run-scoring hit for insurance.
Harrell threw 99 pitches through seven innings and manager Bo Porter chose to go to the bullpen for the eighth in a scoreless game.
"I wasn't going to send him back out there and put him in position to get the loss," Porter said. "You send him back out there, now he's at 115 or 116 pitches with men on base. Now, you're going to bring somebody else into the game and he's in position to get a loss. He did a great job. It's a positive start for him and we got him out of the game on a good note."
Harrell was making his 14th start and it marked the first time this year he has not surrendered an earned run. It was quite a recovery for Harrell after he loaded the bases in the first and threw 51 pitches through two innings. Over his last five innings, Harrell threw just 48 pitches and retired 12 in a row at one stretch.
"I started pounding the zone and used my sinker to get ahead," Harrell said.
The Astros couldn't reward Harrell's effort with a victory because Kansas City starter Luis Mendoza also threw seven innings of shutout ball. That left the outcome in the hands of the respective bullpens and -- for the second time in the weekend series -- the Royals' bullpen came out on top.
Ambriz got the first hitter in the eighth, but was then victimized by the speed of Royals second baseman Chris Getz. When Getz smacked a grounder into the hole on the right side, second baseman Jose Altuve made a diving stop. But throwing from his knees, Altuve was unable to get Getz streaking down the line. Getz then stole second and scored on Gordon's single past shortstop Ronny Cedeno.
The Astros (22-42) had their chances offensively, but couldn't get the big hit. Jason Castro struck out with a runner at third and one out in the third. Houston put the first two hitters aboard in the seventh, but Mendoza retired the next three. In the eighth against reliever Aaron Crow, the Astros again had two on before Carlos Corporan lined into a double play.
"[Mendoza] did a really good job of pitching us backwards," Porter said. "When we were ahead in the count, it was a lot of offspeed stuff. He settled in and did a good job of mixing his pitches."
The silver lining in the shutout loss was the effort of Harrell. The Astros can only hope the native Missourian will build on Sunday's outing in his home state.
Harrell detected a bit of a mechanical flaw after three consecutive hitters reached in the first inning.
"I was leaning back a little bit," Harrell said. "I needed to stay taller and make sure my body was in sync with my arm. I was kind of flying off the ball a little bit. I came in and looked at that. When I went back for my warmups, I knew that was something I needed to work on."
Having his personal rooting section in a road game spurred Harrell on.
"It was really nice getting to pitch before a lot of friends and family," Harrell said.
Getz was relieved to see that Harrell was out of the game when Getz came up in the eighth with the goal of igniting a rally.
"Harrell pitched a really nice game," Getz said. "He's a great sinkerballer, so you can't really try to pull a sinkerballer or you just beat it into the ground. That guy [Ambriz] had a straighter fastball, so I was able to pull something and beat it out."
The Astros headed on to Seattle knowing they were in position to win two of the three games against the Royals. But the offense didn't respond for Jordan Lyles on Friday or Harrell on Sunday.
"We needed a couple of hits here and there," first baseman Carlos Pena said. "We aren't catching any breaks right now, but it'll come."