Voit's game-winning hit came off Royals relief pitcher Greg Holland in the 6-5 win Wednesday in New York. The Yankees trailed 5-4 at the start of the inning.
Catcher Gary Sanchez had hit a solo homer to tie the score two at-bats before Voit's game-winner.
"The last few games, I keep hitting the top of the wall, but, hey, it doesn't matter," Voit told reporters. "I don't care if I hit it 22 mph or 110 mph, as long as I get the job done -- that's all this team needs."
Royals designated hitter Ryan O'Hearn hit a two-run homer in the top of the first inning for the first runs of the game. Yankees outfielder Clint Frazier tied the score with a two-run double in the bottom of the fourth.
Royals first baseman Carlos Santana answered with a solo homer in the top of the eighth. Yankees second baseman Rougned Odor followed with a 406-foot, two-run blast off Royals relief pitcher Jake Brentz in the bottom of the inning.
The Royals took the lead back in the top of the ninth. Sebastian Rivero took a walk with the bases loaded to tie the score at 4-4. O'Hearn brought in Whit Merrifield with an RBI single in the next at-bat to give the Royals a late 5-4 edge.
Holland started the bottom half of the inning by striking out Yankees slugger Aaron Judge. He then managed a 1-2 lead in the count against Sanchez. The Yankees catcher hit Holland's fifth pitch to left field for a 379-foot solo homer, tying the score.
Giancarlo Stanton singled to right field in the next at-bat. Wade replaced Stanton as a pinch runner and came around to score on Voit's single six pitches later.
Voit went 1 for 5 with an RBI and three strikeouts. Frazier and Odor drove in two runs apiece for the Yankees.
O'Hearn went 2 for 5 with three RBIs and a run scored for the Royals. Santana went 2 for 3 with an RBI, a run scored and two walks.
Yankees starter Michael King allowed three hits and two runs in 4 2/3 innings. Royals starter Danny Duffy allowed no hits and no runs in two innings.
The Yankees (39-34) will host the Royals (33-39) in the final game of the series at 1:05 p.m. EDT Thursday at Yankee Stadium.