New York ? Once the New York Yankees finally broke through with the bats, they turned it into an easy night for Ivan Nova.

Robinson Cano hit a three-run homer, Lyle Overbay added a grand slam and New York snapped out of its offensive funk with an 8-1 victory over the Kansas City Royals on Wednesday.

“We needed that really bad,” Cano said.

Nova delivered another impressive pitching performance and the Yankees, held to one run each of the previous three days, stopped a three-game slide.

But it wasn’t all good news. Depleted by injuries all season, New York had two more players get banged up in slumping Travis Hafner and speedy Brett Gardner.

Hafner came out of the game with a bruised left foot, while Gardner departed with a bruised right leg after getting hit by a pitch for the second time. The team said X-rays on both were negative and they were day to day.

Hafner got hurt while swinging in the indoor cage during the middle innings. He cranked the pitching machine up near 100 mph and fouled one off his foot.

“Just kind of a freak incident,” Hafner said, adding he thinks he should be all right. “That’s a first.”

Said manager Joe Girardi: “I don’t get summoned to the cage very often.”

Gardner also walked twice and scored two runs. He reached base all four times from the leadoff spot.

Nova (4-2) yielded only four singles and a double in eight innings for his second win in three solid starts since returning from the minors. He struck out six and walked two.

“He has that kind of stuff that he can be one of the best in the game,” Cano said.

The right-hander was coming off his first career complete game, a three-hitter against Baltimore last Friday that included 11 strikeouts.

“Same thing. Pretty good downhill with his fastball, really good curveball and mixed in a few changeups. I mean, that’s kind of the formula for him. When his fastball’s like this, he’s going to get a lot of outs,” Girardi said. “It should help his confidence. … He’s back on track.”

Cano and Overbay both connected off Wade Davis (4-8), who dropped his third consecutive start.

“I fell behind when I was in the stretch with runners on. I left bad pitches up in the zone,” Davis said.

With the Yankees still waiting for injured stars Derek Jeter, Curtis Granderson and Alex Rodriguez to return, Girardi said he wasn’t particularly tempted to shuffle his makeshift lineup in an attempt to spark the offense.

“What would you suggest?” he asked a reporter before the game. “This is what it is.”

No changes necessary on this night.

Gardner drew a leadoff walk in the first and scored on a wild pitch. With two outs in the third, Cano stayed back on a 1-1 breaking ball and drove it just over the left-center fence. It was the 21st homer of the season for Cano, the American League captain for the Home Run Derby next Monday night across town at Citi Field.

Cano singled to start the sixth and New York loaded the bases with none out for Overbay. He lofted a full-count pitch a few rows deep to the opposite field in left for his fourth career slam and first since May 10, 2006, with Toronto.

“The little things set us up for those big hits,” Overbay said. “I’m just glad I put a swing on it and put it in the outfield for (at least) a sac fly. I can’t remember how many times I’ve struck out with the bases loaded.”

Davis crouched in disappointment next to the mound and was pulled from the game. He allowed eight runs, matching a career high, and six hits in his second ineffective start this season against the Yankees. They tagged him for seven runs and seven hits May 10 during a three-game sweep in Kansas City.

“Wade threw fine. The numbers don’t always tell the story,” Royals manager Ned Yost said.

Meanwhile, Nova was cruising thanks to a 93-95 mph fastball and sharp curve. Helped by Luis Cruz’s diving grab at third base, he retired 12 straight before loading the bases with two outs in the fifth. After a visit from pitching coach Larry Rothschild, the right-hander set down Alcides Escobar on a shallow fly.

Cano doubled off the very top of the right-center wall in the seventh, but was thrown out by Lorenzo Cain trying to stretch it into a triple.

Cano also had some fun with double-play partner Eduardo Nunez on a second-inning popup that was caught by the shortstop on Cano’s side of second base. Cano casually folded his arms in mock disbelief as the ball descended and then shot Nunez a nasty look before cracking a smile.

Eric Hosmer hit an RBI double with two outs in the eighth for Kansas City.

NOTES: All-Star C Salvador Perez was rested by the Royals in favor of George Kottaras. … RHP Ervin Santana (5-5, 2.90 ERA) faces Yankees LHP Andy Pettitte (6-6, 4.37) in the series finale Thursday afternoon. Pettitte is 15-3 with a 3.40 ERA against Kansas City, including 10-0 in 14 starts since Sept. 4, 2000. … Jeter (ankle) went 0 for 3 with a throwing error at SS in seven innings for Triple-A Scranton/Wilkes-Barre, his fourth rehab game. He is expected back with the Yankees in the next few days, but Girardi would not confirm a report that indicated the plan is for the captain to return Friday. … Rodriguez (hip surgery) went 1 for 3 with an RBI single as the DH for Class-A Tampa, making him 2 for 15 during his rehab assignment. It was his first RBI in six minor league games. Rodriguez said he’ll play third base Thursday for Tampa and then get a day off Friday — leaving him free for a scheduled meeting with baseball’s Biogenesis investigators.