Bubic (6-6) gave up only two hits and a walk while striking out six. He allowed just three earned runs over 23 innings in four outings against Detroit this season.
''I've been in a pretty good rhythm lately,'' Bubic said. ''Just using the fastball as effectively as I can. Today I probably threw more fastballs than I usually do. Maybe that's a product of facing this team again or just feeling good with it.''
Bubic doesn't have an overpowering fastball but he located it well.
''He did fill up the strike zone early,'' Detroit manager A.J. Hinch said. ''He attacked us with his fastball and we just didn't generate a lot of offense. Up until the last inning, I think our only hits were with two outs or erased on a double play.''
Scott Barlow survived a shaky ninth for his 16th save.
Whit Merrifield had three hits and scored for Kansas City. Andrew Benintendi contributed two hits and an RBI.
Isaac Paredes had two hits and drove in Detroit's lone run.
Tigers starter Wily Peralta (4-4) carried a 16-inning scoreless streak into the game. The Royals halted it in the first inning on Benintendi's RBI single.
Kansas City left the bases loaded twice in the first three innings before pushing across another run in the fourth on Nicky Lopez's sacrifice fly.
Paredes had an RBI double in the ninth but the Tigers left the bases loaded when Barlow struck out pinch-hitter Harold Castro.
''A little nerve-wracking there,'' Barlow said. ''Overall, I was happy with bouncing back and making pitches when I had to.''
Paredes' extra-base hit might have also scored Eric Haase from first base with the tying run, but it bounced into the left-field stands in foul territory for a ground-rule double.
''That's pretty lucky (for the Royals),'' Hinch said. ''Nothing really you can do about it. That's the rule. I think the side wall was just low enough for them and not high enough for us.''
The Royals won the weekend series 2-1 and the season series 11-8.
The Tigers placed OF Victor Reyes on the 10-day injured list due to a right groin strain and recalled SS Zack Short from Triple-A Toledo.
Royals: Rookie RHP Jackson Kowar (0-4, 11.45 ERA) will start at Cleveland on Monday in the makeup of a game postponed last Wednesday. Kowar has allowed at least five earned runs in his last three outings.
Tigers: RHP Matt Manning (4-6, 5.73 ERA) will start against the Chicago White Sox on Monday in the makeup of a game postponed last Wednesday. Manning also pitched against the White Sox last Monday, allowing three runs in five innings in a no-decision.
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