BC (14-8-0) will face Drake in the tournament's round of 16 on Sunday, Nov. 29. Game site and time are to be announced.
Reddick one-timed a cross along the ground from freshman Kyle Bekker with his right foot at 7:43 for the gamewinner. Freshman goalkeeper Justin Luthy recorded three first-half saves to earn the victory, his ninth shutout of the season.
St. John's outshot the visiting Eagles 12-10, with a 9-3 first-half edge. BC totaled seven second-half shots to the Red Storm's three.