Maddon was tossed after exchanging words with Emmel following a warning that was issued to both benches when Rays starter Matt Moore threw a 95-mph fastball near Curtis Granderson's head in the third.
The Yankees had just taken a 5-0 lead on Moore and the Rays. Granderson's at-bat, which ended with a walk, immediately followed Russell Martin's three-run homer.
"I'm just telling [Emmel], 'That's not necessary. You don't have to set any warnings,'" Maddon said. "[Moore's] not throwing at anybody right there. All I kept saying was, 'That's not necessary,' and then I said, 'You're wrong,' and then he threw me out. So at that point, I had to make a few other points once I got out there."
It was Maddon's fourth ejection of the season and his 27th in seven years as the Rays' manager.
Designated hitter Matt Joyce was also ejected in the top of the eighth inning for arguing balls and strikes with Emmel after Joyce struck out looking to end the inning.