The non-league game was close throughout with the Minutemen holding a 32-28 edge at halftime.
Concord was led by senior Marcus Walton, who scored 24 points.
The Minutemen improved to 14-6 overall while Miramonte fell to 13-7.
Next up for Concord is Mt. Diablo High on Friday night. The game begins at 7 p.m. at Mt. Diablo.
For more scores, go to the Contra Costa Times prep sports website.