The Hawkeyes, who routed Maine 46-3 last week, looked even better against the Golden Panthers. Stanzi, who got the start over Jake Christensen, was 8-of-10 for 162 yards in less than a half as the Hawkeyes (2-0) racked up 512 yards and led 35-0 at halftime.
Christensen came on and was 8-of-12 for 99 yards and one touchdown. But it was clear Stanzi has taken the lead in the competition to be Iowa's starter the rest of the season.
FIU (0-2) had no answer for Iowa's defensive front, which stopped the Golden Panthers all day. The Hawkeyes had six sacks, and when they weren't slamming quarterbacks Paul McCall and Wayne Younger to the turf they were stuffing running lanes and forcing both to hurry throws.
Younger came off the bench and was 11-of-20 for 107 yards to lead FIU, which lost for the 25th time in 26 games dating back to 2006. The Golden Panthers have now been outscored 82-10 this season.
The Hawkeyes rolled up 209 yards of total offense and a 21-0 lead in the first quarter.
Iowa scored on its opening drive for the second straight week, after failing to get any points on opening possessions last season. Greene capped that drive with a bruising 11-yard TD run, bouncing off a number of defenders before stretching the ball over the goal line.
Stanzi made it 14-0 with a 59-yard touchdown pass to Derrell Johnson-Koulianos. Stanzi hit Johnson-Koulianos in stride about 40 yards downfield, and Johnson-Koulianos used some nifty footwork to sidestep defenders near the out-of-bounds line and reach the end zone.
Christensen came in for Stanzi and threw a third-down pass into the turf on his first attempt, drawing a chorus of boos from the Kinnick Stadium faithful. That was quickly forgotten, as Paki O'Meara pushed Iowa's lead to 21-0 with a 17-yard TD run late in the first quarter.
Christensen, who played just two series in the first half, got the nod to start the second half. He pushed the lead to 42-0 on a 23-yard TD pass to Sandeman early in the fourth quarter.
Greene, who spent last season at a junior college because of academic trouble, passed the 100-yard mark for the second straight game. Sandeman's touchdown grabs were the first two of his career.