After going hitless in his first seven at-bats with the Yankees, Encarnacion -- who was acquired Saturday night from the Seattle Mariners in exchange for minor league pitcher Juan Then -- homered in the eighth inning of Tuesday's 6-3 victory over Tampa Bay.
The home run was Encarnacion's American League-best 22nd blast of the year.
"It feels better when you win," Encarnacion said. "It's all about having fun. That's what we need. Have fun and play the game right."
Encarnacion's first Yankees home run came with a custom home run call from radio announcer John Sterling, who declared it was "una celebracion for Edwin Encarnacion!"
Encarnacion is hitting .237 with 22 home runs and 50 RBIs this year.
New York moved to 45-27 with their fourth straight victory. The Yankees have a 2 1/2-game lead over the Rays for first place in the AL East Division.