Davis scored 18 points, grabbed 10 rebounds and made 10 of Tulane's 23 free throws.
Tarrant, who recorded a game-high four steals, knocked down 3 of 4 3-pointers. His trey with 7:52 left in the first half gave Tulane a 19-17 lead and sparked a 20-4 run for the Green Wave.
Tulane (3-1) led 39-21 at the break.
Chicago State (1-3) would not get any closer as Tulane built leads of 16, 23, and 29 in the second half.
Tulane shot 24 of 52 from the field and made 23 of 27 free throws. Chicago State shot just 34.5 percent (19 of 55) from the field and committed 23 turnovers. The Green Wave scored 16 points off those errors.
Corey Gray led the Cougars with 16 points.