Cordell Pemsl scored 15 points to lead four Hawkeyes in double figures.
Reginald Gee had 15 to lead Alabama State (0-2).
The Hawkeyes pushed the lead to 30 a little less than four minutes into the second half and to 40 with 10:52 to go.
Iowa (2-0) dominated every facet of the game.
The Hawkeyes outrebounded the Hornets 53-38 and forced 17 turnovers. The Hawkeyes had 25 assists to the visitors' 10.
Alabama State shot 36.5 percent from the field and made just 4 of 14 from beyond the arc.
The Hawkeyes rolled to a 47-22 halftime lead, and the margin could have been larger had they not missed nine of their 23 free-throw attempts. Iowa shot 51.5 percent from the line for the game.
Fouls were again a problem for the Hornets.
They were called for 14 in the first half, after committing 26 in their Friday loss to Mississippi State.
Iowa broke open the game with a 20-0 run to go up 31-11 with 9:36 left in the first half.
Alabama State missed 14 consecutive shots during a seven-minute stretch of the first half.
Iowa forward Connor McCaffrey missed his second straight game with an ankle injury.