Harrell, who sat out last season after transferring from Virginia, scored 15 points in the first half to help the Tigers (1-0) snap a 10-game losing streak.
Auburn opened the second half on a 9-0 run to build a 46-29 lead and coasted the rest of the way, pushing the margin as high as 27 points.
The Colonels (0-1) shot just 34 percent (19 of 56) from the floor and fell to 2-45 against Southeastern Conference teams. Auburn was 22-of-46 shooting (48 percent). Both teams are trying to rebound from nine-win seasons
Denson made 11 of 14 free throws for the Tigers. Asauhn Dixon-Tatum had eight points, eight rebounds and four blocked shots after gaining some 25 pounds in the offseason.
Harrell scored Auburn's first two baskets in his debut with a 3-pointer and a layup. He and Denson combined to score 24 of Auburn's first 31 points.
Harrell is expected to make up much of the scoring load with the departure of top scorer Frankie Sullivan, and delivered in his debut.
Outrebounded in the first half, Auburn finished with a 39-34 edge on the boards.
Nicholls State kept it close in the first half, trailing 37-29 at halftime. But the Colonels missed their next six field goal attempts out of the locker room, with Smith hitting four free throws before breaking the drought from the field with a 3-pointer.
The Tigers built a 35-24 lead before the half on Dixon-Tatum's two free throws with 2:24 left.
Carpenter responded with his third 3-pointer to help cut Auburn's halftime lead to single digits.
It was the third straight year Nicholls State has opened against an SEC team.