Wernon Goodridge scored 15 points, Terrell Williams 14 and Yves Mekongo Mbala 10 for the Explorers (7-5), who never trailed.
Devon Austin scored 13 points and Antoine Pearson 11 for the Jaspers (7-5).
La Salle held a 19-16 lead midway through the first half when Green scored 11 of his points in a 23-5 run. He capped the outburst with a layup that gave the Explorers a 42-21 lead with 2:28 remaining.
La Salle shot 69 percent from the field in the first half while the Jaspers struggled, hitting 37 percent of their shots.
The Explorers led 48-31 at the break. Manhattan (7-5) scored eight straight early in the second half to close within 52-39, but Green sank a free throw and added a layup that extended La Salle's advantage.
La Salle holds a commanding 38-7 record in the series.