The Rays second baseman went 2 for 5 with three RBIs and two runs scored in the 5-2 series finale victory Wednesday in New York City.
Tampa Bay now holds a 4 1/2-game division lead over second-place New York with 22 games remaining in the shortened 2020 MLB season.
The Rays won two of three games in the series to build on their division lead. Brosseau's homers came a day after Yankees pitcher Aroldis Chapman threw a 101-mph pitch over his head during a heated exchange at Yankee Stadium.
"It felt amazing," Brosseau told reporters. "I'm glad I could help my team, especially with the stakes that we had [Wednesday]."
Manuel Margot doubled in the first at-bat of the game before Rays left fielder Randy Arozarena settled in against Yankees starter Jordan Montgomery. Arozarena earned a 3-1 lead in the count before he smashed Montgomery's fifth offering over the left field fence for a two-run homer.
Austin Meadows singled in the next at-bat, which prompted Brosseau to walk to the batter's box for his first at-bat of the night. Montgomery picked up two quick strikes on the Rays infielder before Brosseau worked the count even.
Brosseau then blasted a 2-2 curveball deep the left field for a 420-foot, two-run shot. Brosseau's bomb traveled 105-mph and left the field in 5.5 seconds, according to Statcast. The homer also gave the Rays a 4-0 lead.
Montgomery was pulled from the game before the second inning. Neither team plated another run until Brosseau returned to the plate in the top of the fourth frame.
Yankees relief pitcher Jonathan Holder began the inning with back-to-back strikeouts before Brosseau fouled off his first offering of his exchange with the right-hander.
Brosseau then belted an 0-1 Holder fastball to right center field for a 418-foot solo shot and 5-0 Rays lead.
Yankees designated hitter Clint Frazier hit his fourth home run of the season in the bottom of the sixth frame for New York's first run. D.J. LeMahieu plated Brett Gardner for the final run of the game in the bottom of the ninth inning.
Rays starter Charlie Morton pitches two hitless and scoreless innings, but was not on the record for a decision. Montgomery allowed five hits and four runs in 2/3 of an inning to move to 2-2 on the season.
Arozarena went 1 for 3 with two RBIs, a run scored and a walk for the Rays. Shortstop Willy Adames also had two hits in the win. Gio Urshela went 2 for 4 for the Yankees.
The Yankees (20-15) will face the rival New York Mets at 4:10 p.m. EDT Thursday at Citi Field in Queens, N.Y. The Rays (26-12) host the Miami Marlins at 6:40 p.m. EDT Friday at Tropicana Field in St. Petersburg, Fla.