Greene, who missed last season due to academic issues at a junior college, scored on a 1-yard plunge on the Hawkeyes' first possession, capping a 69-yard drive, and Iowa was on its way to an easy win.
The Hawkeyes overpowered the Black Bears (0-1) with 245 yards rushing, including a 19-yard TD run by Hampton on his first career carry.
Iowa led 22-3 at halftime and turned the game into a blowout in a 15-second stretch early in the fourth quarter. Paki O'Meara capped a 10-play-drive with a 1-yard run to make it 32-3, and after an interception by a Pat Angerer, Hampton scored to make it 39-3 with 14:43 left.
Hampton added a 22-yard TD run with 3:29 left, and finished with 68 yards on nine carries.
Jhamal Fluellen ran for 104 yards to lead Maine, which lost its fourth straight to a Football Bowl Subdivision team after winning at Mississippi State 9-7 in 2004. The 43-point loss was Maine's worst in seven meetings against FBS opponents.
Christensen started all 12 games in 2007 and had a tenuous hold on the No. 1 job after fall camp. Stanzi came in after Christensen threw a second-quarter interception, but Christensen bounced back in the second half, helping the Hawkeyes put the game out of reach.
Christensen was 9-of-15 for 122 yards, with one touchdown and one interception. Stanzi was 9-for-14 for 90 yards, playing most of the second quarter and re-entering the game in the fourth quarter.
Iowa's Bradley Fletcher came down with the interception off a tipped ball the first time Maine got the ball, and Christensen found Brandon Myers for a 4-yard touchdown pass to make it 14-0 with 3:37 to go the first quarter.
Christensen was 5-of-9 for 60 yards in the first half. But when he missed, he missed badly -- including an underthrow to Paul Chaney Jr. that Maine picked off at its own 3.
A.J. Edds bailed out Christensen with a safety that made it 16-0 with 12:31 to go in the second quarter, but Stanzi got the call for the rest of the half. He led the Hawkeyes to a pair of field goals to push Iowa's lead to 22-0.
Maine's Bryan Harvey hit a 40-yard field goal as half ended for the Black Bears' only points.
Adam Farkes was 9-of-22 for 83 yards and two interceptions for Maine.