Escobar was signed by the Mets as a non-draft amateur free agent in 1995 and made his debut in 2001. At the end of the season, he was traded to the Indians as part of an eight-player deal that sent Roberto Alomar to the Mets. Escobar missed the entire 2002 season after tearing his left anterior cruciate ligament (ACL) during Spring Training. In 2003, he recovered from a slow start at Triple-ABuffalo Bisons collecting 24 home runs and 78 runs batted in, and looked strong for the Tribe in September and played in 28 games.
In the minors, Escobar was an All-Star in the 'AAA' International, 'AA' Eastern and 'AA' South Atlantic leagues, and he also was selected by Baseball America in the 1998 All-Stars team. Escobar was demoted by the Nationals during Spring Training after hitting just .103 (3-for-29) with two RBIs. He said he was not getting enough playing time in spring training. "I'm not swinging the bat. I have to work my way back," Escobar said. "I'm getting used to being on the field every day. It's a combination of everything." Baseball America rated him as a top prospect for three years,