Garrett Atzenweiler pushed Northwestern State (6-5, 4-3 Southland) ahead with a 1-yard touchdown run and Adkins threw scoring strikes of 17 yards to Zach White and 24 yards to Cody Jones for a 28-7 halftime lead.
Adkins connected with Jones and Tuff McClain in the third quarter, and scored on a 3-yard keeper with 9:31 remaining.
Adkins went 17 of 20 - completing his first nine attempts - without an interception.
Jones had four receptions for 68 yards. Daniel Taylor finished with 80 of the Demons' 300 rushing yards.
Michael Henry paced Nicholls (0-11, 0-7) with 146 yards on 29 carries, including a 19-yard touchdown on the games' opening drive. Beaux Hebert hit Demon Bolt for a 2-yard score to make it 35-14 in the third.