Two layups by Warney and a 3-pointer by Jackson launched a 14-0 run that gave the Seawolves (5-2) a 33-19 lead with 5:04 remaining in the first half. Warney had 13 points and Jackson 11 in the half.
Johnathan Gray scored 17 points to lead the Big Red (3-5), who never got closer than 11 points in the second half.
Other than Gray's 6-for-8 shooting, including 5 of 6 from 3-point range, Cornell shot 26.3 percent (10 of 38).
Tommy Brenton added nine points, six rebounds, six assists and three steals for Stony Brook, as coach Steve Pikiell picked up his 100th victory against 120 losses in eight seasons with the Seawolves. In the past three-plus seasons his record is 64-39.