The 10-1 win on Wednesday at Yankee Stadium also prevented the Red Sox from clinching the American League East.
Miguel Andujar hit a solo home run in the bottom of the second inning to give the Yankees their initial 1-0 advantage. Aaron Judge plated Voit and Gary Sanchez when he reached on a fielding error later in the same inning.
New York held the 3-0 advantage through the top of the fourth inning, before Voit led off the bottom of the frame.
He fell down in the count 0-2 to Red Sox starter David Price before ripping a 92.9-mph fastball into the right field seats for his ninth long ball of the season. The blast traveled 341 feet, according to Statcast.
Andujar led off the bottom of the sixth frame by flying out to left field for the Yankees. Sanchez followed by taking a walk before Voit walked to the plate as the third batter of the frame. Price again earned an 0-2 lead in the count, before Voit worked it to 2-2.
Price then tossed in an 87.6-mph changeup, which Voit sent to right field for his second long ball of the game. After a brief umpire review, the two-run shot was allowed.
"Tonight it was a little windier, so you didn't know," Voit told reporters. "I thought I got that last one more than I did and it barely went out. Luckily it went over. You watch every guy hit a ball to right field, they're always looking at the outfielder and judging it. There's definitely cheap home runs, but you've got to take advantage of it."
The Yankees added on to the lead with a two-run triple from Aaron Hicks in the sixth inning. Greg Bird scored Voit with an RBI ground out in the bottom of the eighth inning. Hicks singled in Gleyber Torres for the Yankees' final run in the same frame.
Voit went 4-for-4 on the night with four runs scores and three RBIs. He is now hitting .308 on the season with 10 home runs and 23 RBIs.
Luis Severino earned his 18th win of the season by allowing six hits and one run in seven innings for the Yankees.
The Yankees and Red Sox continue the American League East showdown at 7:05 p.m. on Thursday at Yankee Stadium.