The Stags (2-2) led 31-29 at halftime, before the Crusaders scored the first five points of the second half to take the lead.
Fairfield then went on a 24-8 run to take a 13-point lead, 55-42, with 8 minutes remaining. The Stags increased their lead to as much as 25 points down the stretch.
Barrow, who was 7 of 11 from the field, scored 13 of his points in the second half.
The Stags shot 54.5 percent (30 of 55) from the field and outrebounded the Crusaders 39-29, including a 24-13 rebounding advantage in the second half.
Phil Beans and R.J. Evans led Holy Cross with 14 points apiece. The Crusaders (1-3) were just 8 of 24 from the field in the second half, including 1 of 8 from 3-point range.