Baltimore ? The Kansas City Royals played an entire game without an assist, a rarity in the big leagues.

Far more commonplace is Royals ace Zach Greinke pitching well and not having a win to show for it, which is exactly what occurred for the fifth time this month in Baltimore’s 7-3 victory Wednesday night.

The last team to go a game without an assist was Tampa Bay on May 17, 2003, also in a loss — eight innings in the field — to Baltimore, according to STATS LLC. Only five teams in major-league history have done it for at least nine innings in the field.

The Orioles hit only two grounders, both of which were handled by first baseman Billy Butler before he touched the bag himself.

Greinke, meanwhile, pitched six innings of five-hit ball and left with a 3-2 lead. But Baltimore went ahead with a three-run seventh that kept the AL ERA leader winless in July.

“We have found a way to lose a lot this month no matter how it is. Just been a real bad month for everyone,” said Greinke, referring to the Royals’ 7-17 record in July.

Adam Jones homered and drove in three runs, Nick Markakis also had three RBIs, and the Orioles got a decent start from 21-year-old Chris Tillman in his major-league debut.

Tillman yielded three homers, but those were the only runs he permitted over 42/3 innings. Tillman gave up only five homers in 18 starts this season with Triple-A Norfolk.

“I feel like next time I’ll be a little more comfortable up there,” he said. “I’ll have my feet underneath me. Hopefully, my breaking stuff will be there.”

Greinke went 0-3 in five starts this month despite allowing only nine runs in 32 innings. Unfortunately, Kansas City scored six runs in July while he was in the game.

In this one, Greinke permitted two runs in the first before limiting Baltimore to one hit over the next five innings. By the time he left, he had thrown 116 pitches.

“Greinke is as tough as anybody in the big leagues, but we worked him,” Orioles manager Dave Trembley said. “We got his pitch count up, and we worked him.”

Although Greinke’s ERA rose slightly to 2.08, his seven strikeouts moved him past Steve Busby into eighth place on the Royals career list with 661.

Alberto Callaspo, Miguel Olivo and Mike Jacobs homered off Tillman, who allowed seven hits and a walk before leaving to a standing ovation from the crowd of 19,741.

“That was pretty special. It feels good,” the right-hander said. “I’ve heard a lot about these fans here. Getting into the dugout and the guys even joking with me then, it was definitely a good feeling.”

Tillman was the fifth Orioles starter to make his debut this year — and the only one who didn’t earn a victory. But Baltimore has won each of those games.

Robinson Tejada (1-1) followed Greinke and promptly walked the first two batters in the seventh. Jones then doubled in a run off John Bale, and Markakis followed with a line-drive single that easily cleared the drawn-up infield.

Markakis and Aubrey Huff added RBI singles in the eighth.

Matt Albers (2-4), who rescued Tillman with two on in the fifth, gave up one hit in 21/3 innings and Jim Johnson worked two innings for his second save.

Greinke was fortunate to get out of the first inning in a 2-0 hole. After Brian Roberts led off with a single, Jones homered to left — his third first-inning drive in as many games. Baltimore then used a double, a walk and a hit batter to load the bases before Gregg Zaun struck out.

Tillman got off to a good start by retiring the side in order in the first, but Callaspo and Olivo hit solo homers in the second to tie it. Callaspo’s homer extended his hitting streak to a season-high 11 games.

Jacobs’ 14th homer put the Royals up 3-2 in the fourth.

Notes: Cincinnati was the last team to go without an assist while playing at least nine innings in the field, in 1997. … To make room for Tillman, the Orioles put LHP Rich Hill (shoulder) on the 15-day disabled list. … KC RHP Gil Meche (back strain) threw 52 pitches in a simulated game Wednesday and could be sent to the minors for a rehab assignment if he feels OK Thursday, manager Trey Hillman said.