Ordonez's homer in the ninth was his first extra-base hit after 17 singles, and he now has 14 home runs and 62 RBIs in 78 games at Kauffman Stadium.
Miner (2-1) picked up the victory, going five-plus innings and allowing one run on three hits for Detroit. Miner is 3-0 with a 0.39 ERA in six games, including three starts, at Kauffman Stadium.
"I think it's mostly just coincidence," Miner said. "I've pitched here quite a few times and had some success. I definitely don't mind coming to KC."
Neither does Laird, who had a career .382 average against the Royals and is 5-for-7 in the first two games of the series.
"I've always liked coming here and playing," Laird said. "It's a big yard and I see the ball real well here. I'm just putting good swings on the ball and the ball is finding holes for me."
"He was in trouble and got the good sinker, got the groundball right at somebody," Tigers manager Jim Leyland said. "That was the biggest at-bat of the game, no question."
Leyland had Juan Rincon warming up after the walks, but Miner retired eight in a row to make it into the sixth.
"I thought, let's try to get out of this," Miner said. "It didn't help Teahen was coming up. He's probably the one guy in the lineup I want to face the least in that situation. It ended up working out.
"Teahen hits me real well and always seems to have good at-bats against me. I definitely didn't want to get 3-2 on him. I was fortunate to get the ball down and got a groundball. The last thing you want to do is when the team gets you runs is go out and walk the first two guys of the inning, but I did it. I tried to stop the damage. I wanted to keep it to a minimum and was fortunate to get the strikeout and double play."
The Tigers broke the game open with a four-run sixth, which included a two-run triple by Josh Anderson and a two-run double by Placido Polanco. Anderson's triple, which scored Laird and Brandon Inge, finished Royals starter Kyle Davies.
"The home runs weren't very good pitches," Davies said. "It was a change up to Laird, up in the zone, middle in. Granderson hit a fastball out over the plate. I didn't have the best changeup and the fastball was not very effective. I didn't have very good location."
Davies (1-1) gave up seven runs on eight hits, including two home runs, while walking two and striking out two. He was replaced by Robinson Tejeda, who yielded Polanco's double, which scored Anderson and Granderson.
"I'm disappointed Kyle didn't make adjustments," Royals manager Trey Hillman said. "Miner settled in."
The Royals scored their only run in the third when Crisp scored on Mike Jacobs' ground out. The Royals went 0-for-6 with runners in scoring position.
Royals RF Jose Guillen, who had been on the disabled list with a hip injury, was activated. C Brayan Pena was designated for assignment. ... The Tigers improved to 21-8 at Kaffuman Stadium since the start of the 2006 season. ...The Royals are 8-4 when RHPs Zack Greinke, Gil Meche and Davies start. They are 1-4 when anyone else starts. ... Royals 2B Alberto Callaspo singled in the second to extend his hitting streak to eight games.