Monasterio went 1-for-2 with a double in Sunday's 3-2 loss to Cincinnati.
Monasterio, who made his first appearance of the regular season, pinch hit for Marcelo Mayer in the seventh inning against a right-handed reliever and remained in the game at second base. The backup gave the Red Sox some hope in the ninth inning with a one-out double, but he was stranded there. With Mayer routinely hitting the bench against left-handers, Monasterio and Isiah Kiner-Falefa are positioned to be part of a platoon at second base.