Voit homered in the second and fifth innings of the 6-3 triumph and posted a 2 for 4 line at the plate with three RBIs and two runs scored.
The Yankees also picked up wins over their chief rival on Friday, Saturday and Sunday. New York also swept Boston in a three-game series at the start of August.
"That's unique in the history of this rivalry," Yankees manager Aaron Boone told reporters. "I just think it's a stretch where we've had a few really good series against them. They've had some things not go their way, so I don't put a whole lot into it."
Aaron Hicks plated Tyler Wade on an RBI double in the bottom of the second inning to draw first blood for the Yankees. Voit then stepped up to the plate in the next at-bat. The Yankees infielder settled in against Red Sox starter Martin Perez.
Perez worked an even count against Voit before he tossed in a 2-2 changeup. Voit sent the offering into the center field seats for a 428-foot homer. The two-run blast had an exit velocity of 108 mph, traveled 131 feet above the field and took 6.4 seconds to leave the ballpark, according to Statcast.
Red Sox catcher Christian Vasquez then hit an RBI double in the top of the fourth frame to cut the Yankees' lead to two runs.
Thairo Estrada regained a three-run lead for the Yankees with a solo homer in the bottom of the fourth inning.
Voit then returned to the plate for his second homer of the game to lead off the bottom of the next inning. Red Sox relief pitcher Josh Osich began the exchange with a slider outside of the strike zone. He evened the count before he threw Voit a 1-1 cutter. Voit smashed the pitch over the left field fence for a 380-foot homer. That blast left the field in 4.5 seconds and gave the Yankees a 5-1 edge.
Alex Verdugo plated Vazquez with an RBI double in the sixth frame for the Red Sox. Hicks then hit a solo shot for the Yankees in the bottom of the seventh inning. Jonathan Arauz brought in the final run with a ninth-inning RBI double for Boston.
Yankees starter Jordan Montgomery allowed three hits and one run in 3 2/3 innings, but was not on the record for a decision. Perez allowed two hits and three runs in three innings and took his third loss of the season for the Red Sox.
Hicks went 2 for 4 with two RBIs and two runs scored in the win. Vazquez went 2 for 3 with an RBI and a run scored for Boston.