As the very first batter of the game, on the second pitch, Judge connected on a 450-foot bomb deep over the left-field wall.
It was his 53rd home run of the season – and his fourth from his past six games – setting a new career-high after totalling 52 in 2017. He is now eight home runs away from Roger Maris' Yankees record of 61 – set 61 years ago, in 1961.
Judge's shot would be the only score from the first six innings against the Rays as Yankees starting pitcher Frankie Montas continued to find some form following a rough start to his time in New York since being traded at the deadline from the Oakland Athletics.
Montas pitched five near-perfect innings, giving up one hit and no walks to go with seven strikeouts.
The Yankees were able to add an insurance run in the seventh frame thanks to a sacrifice-fly from Oswaldo Cabrera, and although closing pitcher Clay Holmes did give up a run, he was able to complete the save for his 18th of the season.
With the win, the Yankees now hold a five-game lead over the Rays for the AL East lead, and they are six games behind the Houston Astros in the race for the best record in the American League.
Gallen extends historic scoreless streak
Arizona Diamondbacks starting pitcher Zac Gallen is in the midst of the eighth-longest scoreless streak in MLB history as he pitched another seven shutout innings in a 5-1 win against the Milwaukee Brewers.
It has been 41-and-a-third innings since Gallen has allowed a run, and in the process he has become the fourth pitcher in the modern era to pitch six consecutive games with at least six scoreless innings – joining Don Drysdale (Dodgers, 1968), Orel Hershiser (Dodgers, 1988) and Zack Greinke (Dodgers, 2015). With one more scoreless inning, he will break the Diamondbacks' franchise record.
The 27-year-old now sports an 11-2 record this season with a 2.42 ERA and a 0.92 WHIP, establishing himself as one of the top arms in the league.
Giants walk-off after duelling home runs late
The San Francisco Giants treated their fans to one of the most enjoyable spectacles in sport as they ended their 5-3 win against the Philadelphia Phillies with a walk-off home run.
With the Giants leading 3-0 in the eighth inning – thanks in large part to a terrific 10-strikeout performance from ace Carlos Rodon – Phillies catcher J.T. Realmuto erased the deficit with one swing as he connected on a three-run home run.
Needing a run in the bottom of the ninth to win, after Bryce Johnson got on base, Wilmer Flores was the hero for the night as he launched the game-winner hard and flat over the left-field wall to send the fans home happy.