Derek Jeter delivered a bases-loaded single that tied the score and New York rallied from an early two-run deficit to snap a three-game skid. Shut out Monday in the series opener, the Yankees (22-21) went 2 for 7 with runners in scoring position -- one night after they finished 0 for 13 in those situations for their worst performance with RISP since 1990.
"It wasn't that pretty, but that was a good win," said Rodriguez, who struck out with the bases loaded but combined with Mark Teixeira on a game-saving defensive play. "It felt really good to win a game like this. Sometimes you need a game like this to kind of get you on a roll. Hopefully it's a good sign of things to come. We haven't been winning these kinds of games."
New York, which had lost six of seven to drop into a last-place tie with Boston in the AL East, now has eight hits in its last 79 at-bats (.101) with runners in scoring position.
Hughes (4-5) gave up five hits in six innings while striking out seven, beating Royals right-hander Luke Hochevar (3-5) for the second time in 17 days.
"It seemed like nothing was a walk in the park tonight," Hughes said.
The Yankees caught a break when Mike Moustakas lined into a double play to end the eighth. Rafael Soriano worked the ninth for his third save, retiring Alcides Escobar with a runner on third to end Kansas City's five-game winning streak away from home.
Rodriguez fielded Escobar's grounder behind third base and made a high throw across the diamond. Teixeira stretched out his 6-foot-3 frame and kept his toe on the bag as New York got the call on a bang-bang play.
"I don't think there's many other first basemen in the league that could stretch like that and make that play," Hughes said.
"Had 'em all the way," Jeter said.
Cano put the Yankees on the scoreboard with a long solo homer in the fourth, making him 6 for 12 with three home runs and nine RBIs against Hochevar -- including a grand slam May 6 in Kansas City.
New York tagged Hochevar for seven runs and seven hits over 2 1/3 innings in that outing and he entered Tuesday night 0-2 with an 8.83 ERA in four career games against the Yankees.
He hung tough this time, coughing up a 2-0 lead but keeping Kansas City in it when the Yankees appeared poised to finally break loose.
Teixeira, batting seventh for the second consecutive game, singled through the shift to start the fifth and went to second when Jeff Francoeur bobbled the ball in right for an error. Russell Martin was grazed by a pitch and Dewayne Wise reached on a perfectly placed bunt single even though the Royals were expecting a sacrifice.
Once again, the Yankees had the bases loaded and none out with big hitters coming up. They came up empty in that situation during Monday night's 6-0 defeat, but not this time.
Jeter dumped an RBI single into right and Curtis Granderson drove in a run with a groundout, giving New York a 3-2 lead.
"We scored a lot of runs right after that and piled on," Jeter said sarcastically.
Cano was intentionally walked to load the bases for Rodriguez, and the Yankees had a chance to really bust it open. But Rodriguez struck out, drawing boos from the crowd of 37,674, and Raul Ibanez went down swinging as well.
New York never managed another baserunner.
"Hoch pitched great. He did a great job in that inning. They didn't really hit the ball hard," Royals manager Ned Yost said. "He limited the damage big-time."
Kansas City grabbed an early lead when No. 9 batter Humberto Quintero went the other way on Hughes' hanging curve for an RBI double in the second.
Francoeur added a solo shot in the fourth to make it 2-0, his third homer this season and second in two nights at Yankee Stadium.
Hughes has served up 11 home runs in 47 1/3 innings this year. He has allowed at least one in all nine starts, the longest streak by a Yankees pitcher since Jack McDowell in 1995.
Game notes Kansas City put 2B Chris Getz on the 15-day disabled list with a ribcage injury and called up LHP Will Smith from Triple-A Omaha. Smith will start the series finale Wednesday night, his major league debut, against LHP Andy Pettitte. Royals RHP Luis Mendoza, originally slated to start Wednesday, is headed to the bullpen as a long man. ... Irving Falu started at 2B and likely will platoon there with Johnny Giavotella while Getz is sidelined, Yost said. ... Yankees closer Mariano Rivera walked through the clubhouse without crutches but said surgery for his torn knee ligament has not been scheduled yet. Rivera said the last time he had a checkup, the blood clot in his calf was still there. He is taking medication for the clot and doing exercises to strengthen the knee for surgery.