The Red Storm (2-0) opened up an 11-point lead midway through the first half and were not pushed by the Cougars (1-1), who are hosting the eight-team event.
Harrison had a 3-pointer and seven quick points to put St. John's ahead 22-11 with less than six minutes gone. College of Charleston never got closer than eight points the rest of the way.
The two programs had never played before, though they share some significant connections. College of Charleston's basketball architect, coach John Kresse, played at St. John's for Red Storm great Joe Lapchick and was an assistant for Lou Carnesecca.
Kresse came down South, "Noo Yawk" accent intact, and turned the Cougars into giant killers -- most notably defeating Maryland in the 1997 NCAA tournament before nearly toppling eventual champ Arizona in a 73-69 loss.
Kresse spoke with the Red Storm players at coach Steve Lavin's invitation, sharing stories of the program that Lavin's trying to rebuild.
The TD Arena court is named after Kresse, who watched from the stands and was congratulated by people on both sides.
Also in the stands was former Cougars' coach Bobby Cremins, who grew up in New York City before finding success on and off the court down South.
St. John's is in the midst of a four-game opening week, following up Tuesday's season opening victory over Detroit with three games in Charleston.
The Red Storm didn't look like they had tired legs, though, running right from the opening tip.
Christian Jones and Garrett had six points each and Harrison had five as St. John's opened up a 22-11 lead with nine minutes left in the half. The lead grew to 32-18 in the opening half before the Cougars trimmed it to 10 points at the break.
The Red Storm kept the pressure up in the second half and Charleston struggled to stay in the game.
Greene and Harrison had layups to put St. John's ahead 46-28 with 14:42 left.
The Cougars' top player, Andrew Lawrence, was not at his best. Lawrence, the youngest member of the British Olympic basketball team at the London Olympics this summer, was just 1 of 5 from the floor deep into the second half.