Kansas City Royals starting pitcher Zack Greinke delivers during the first inning against the Detroit Tigers. Greinke pitched a complete game, giving up just one run and K.C. won, 6-1, Tuesday in Kansas City, Mo.

Kansas City, Mo. ? Probably the last thing Justin Verlander wanted to do was make Zack Greinke a better pitcher.

But unwittingly, he did.

Greinke paid close attention to the way Verlander shut out Kansas City through seven innings in an easy Detroit win on Monday. Then the Royals ace took the best stuff he’s had all year to the mound on Tuesday night and tossed a six-hitter in a 6-1 victory over the Tigers.

“I’ve been getting worried that teams are going to make adjustments,” said Greinke, who leads the majors in earned-run average, complete games and shutouts. “But I was watching Verlander pitch and even if I knew exactly what he was going to do, I was like, ‘I couldn’t hit him.’ So just stay with what you do and stop thinking so much.

“I think it helped me a lot for today.”

Greinke (8-1) had such good command, he could hardly believe the Tigers scored a run in the first.

“It was one of those days where almost everything was working and they put up a run, so I was like, ‘Just keep it right there. They can’t do too much with you if you keep doing that.”‘

He wound up with eight strikeouts and no walks while his ERA rose from 0.82 to 0.84. In two starts against the Tigers this year, he has allowed one earned run in two complete-game wins.

Greinke threw his fifth complete game this season and the eighth of his career, joining Toronto’s Roy Halladay as the only eight-game winners in the majors.

“He’s got a fastball that he can throw from 93 (mph) and he can hump it up to close to 100 if he wants to,” Detroit’s Brandon Inge said. “He has a sinker if he wants to throw it. He has a changeup. The fun part comes when he has a slow curve and he can make it a little faster.”

With pinpoint control of his varied pitches, Greinke has allowed only seven earned runs in 75 innings this season.

“He’s got a slider that he throws at variable speeds and variable angles,” Inge said. “He’s one of the very few guys I’ve seen that can manipulate the ball the way he wants to.”

Mitch Maier came off the bench and drove in three runs and Jose Guillen homered and drove in two more for the Royals, who crept back to within three games of the first-place Tigers in the AL Central.

Edwin Jackson (4-3), who had won three straight starts, went 61?3 innings and gave up four runs, two of which were unearned because of his two throwing errors to first.

Miguel Cabrera, the major leagues’ leading hitter, was 1 for 3 against Greinke and hit into a double play after Magglio Ordonez’s RBI single in the first.