Jamaica was guilty of poor defending from the outset, and Nosworthy deflected the ball into his own net in the 16th minute before a crowd of 39,628 at Big Swan Stadium.
In his first two games in charge last month, Aguirre lost 2-0 to Uruguay and drew 2-2 with Venezuela. The Asian champion departs on Saturday for Singapore, where it will play Brazil on Tuesday.
Keisuke Honda came close to making it 2-0 with a shot off the crossbar in the 33rd.
Shinji Kagawa, in his first appearance for Aguirre, played deeper in midfield than he does for his Dortmund club, and helped to create chances.