Marvin Jordan added 15 points for the Purple Eagles (3-7), who have won eight straight in the series.
Niagara hit 18 of 19 free throws, all in the second half, with Nelson going 8 for 8.
The Bonnies (5-3) had a 45-25 rebounding edge, but 21 turnovers led to 24 Niagara points.
Although the score was tied five times, St. Bonaventure led only once, at 18-17 with 5:51 left in the first half.
Nelson hit a jumper to give Niagara a 30-26 halftime lead and the Purple Eagles led by as many as 12 in the second half.
Andrew Nicholson had 17 points and 12 rebounds for St. Bonaventure. Da’Quan Cook also had a double-double with 11 points and 10 rebounds.
The series began in 1920-21, with the Bonnies now leading 82-69.