The Jaspers will square off with No. 1 seed Iona for the third straight year in the championship on Monday. Iona won in 2013 and Manhattan last year. The Gaels took both meetings during the 2014-15 regular season.
St. Peter's (16-18) closed to within seven points with 5:26 left, but Manhattan outscored the Peacocks 19-9 from there with a 7-0 run to close the game.
Richards scored back-to-back with a three-point play and 3-pointer to cap a 10-2 run that put the Jaspers up 33-23 at halftime.