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.
Nike Men's Iowa Hawkeyes Black/Gold Team Issue Performance PoloShop
After sloppy conditions hampered Baylor-TCU, more bad weather is coming to Big 12 country and other parts of the nation.
Heather Dinich and Trevor Matich explain how Notre Dame could play their way back into the College Football Playoff.
Michigan State coach Mark Dantonio shares how his team is handling the pressure of being one win away from playing in the Big Ten Championship Game and the status of QB Connor Cook.
Lee Corso discusses how his headgear and College Football Playoff picks haven't gone the way he anticipated this season.
Country music duo Big and Rich get you ready for Week 13 of College GameDay from Stillwater, Oklahoma.
Mitch Sherman breaks down Iowa's win over Nebraska to improve to 12-0 on the season.
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