Gleyber Torres had the game-breaking three-run shot. Aaron Hicks added the inside-the-park kind, the second time he's done it this season. Giancarlo Stanton crushed the moonshot into the fountains, and Gary Sanchez contributed sheer quantity with two solo shots.
Stanton and Sanchez even went back-to-back to cap the night.
''All-in-all, a good bounce-back night for us,'' Yankees skipper Aaron Boone said after the 8-3 win, which gave the Yankees a chance to win their eighth consecutive series in the finale on Sunday.
All those runs made an easy night for Luis Severino (7-1), who scattered three runs on eight hits and two walks over six innings to run his unbeaten streak to seven. The right-hander is 5-0 with two no-decisions since losing to Boston on April 10.
Danny Duffy (1-6) once again threw batting practice for the Royals, allowing the five runs on seven hits and three walks in four innings. It was the fifth time in six starts Duffy has allowed at least four runs, and he still has yet to complete seven innings in a game this season.
''I'm pitching awful right now. I don't know what else to say,'' Duffy said. ''It's horrible. This is brutal. Talk is cheap. I'm terrible right now. It's awful. I'm sick of this (stuff). It's terrible.''
Hicks and Sanchez got the Yankees' homer-happy night going with some small ball - Hicks led off the game with a single and Sanchez drove him in with a two-out double. But the big binge began in the third, when Hicks bounced a long fly ball off the top off the wall and managed to score easily.
He's the first Yankee with two inside-the-park homers in a season since Mickey Mantle in 1958.
''Any time you hear your name with Mickey Mantle,'' Hicks said, ''it's something good.''
Duffy's unraveling came after the Royals answered with two runs in the bottom half.
Clint Frazier, making his season debut, drew a leadoff walk in the fourth. Ronald Torreyes followed with a single, and Torres promptly crushed a 407-foot homer over the left-field bullpen.
It helped atone for a crucial error that Torres made in the Yankees' loss Friday night.
''I'm not a particular guy that homers,'' said Torres, who nonetheless has four since getting called up. ''I just try for good contact, get the best pitch I can.''
Kansas City tried to answer again in the fifth, when Mike Moustakas drove in Ryan Goins with a two-out single. Salvador Perez followed with a double to left, but Moustakas was thrown out in a close play at the plate - replays appeared to show him safe, but the call stood after a video review.
Sanchez tacked on his first homer in the seventh, and Stanton and Sanchez went back-to-back in the ninth. Stanton's mammoth shot landed in the fountains, where a fan appeared to dive in after it.
MORE ON SANCHEZ
The Yankees' catcher also doubled in the first and singled in the third to finish a triple short of the cycle, his second career four-hit game. It was also his third multi-homer game this season.
Duffy floated the possibility of going to the bullpen given his struggles, but manager Ned Yost did not want to discuss options so soon after a game. ''We've got to kind of step back a little bit, simplify a little bit and get back on track,'' he said. ''Do I have an idea how to do that? I think I do. I'll talk to Danny about it in the next day or so and go from there.''
WHAT'S IN A NAME
Torres batted ninth for the Yankees, right behind Torreyes in the order. INF Ramon Torres was on the other bench for the Royals after he was recalled Saturday. Umpire Carlos Torres handled first base.
Yankees: 1B Greg Bird (right ankle surgery) and OF Billy McKinney (left shoulder sprain) could head to Triple-A Scranton to continue their rehab. Yankees manager Aaron Boone said both players at Double-A Trenton are close to returning. ... RHP Tommy Kahnle (right shoulder tendinitis) is expected to pitch for Class-A Tampa on Sunday and could rejoin the Yankees next week in Texas.
Royals: INF Cheslor Cuthbert went on the disabled list retroactive to Wednesday with a lower back strain. Torres was recalled from Triple-A Omaha to fill his roster spot.
The Yankees send RHP Sonny Gray (2-3, 6.39 ERA) to the mound against Royals LHP Eric Skoglund (1-3, 5.58 ERA) for Sunday's series finale. Gray will be pitching on eight days' rest.
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