The Cardinals opened a 31-7 halftime lead, before withstanding a second half rally from the Red Wolves, who cut the margin to 31-24 late in the fourth quarter.
After Arkansas State narrowed Louisville's lead to a touchdown, Chris Philpott connected on a 46-yard field goal to give UofL breathing room in the final minutes.
After Aplin connected with Allen Muse for a 33 yard score to cut the lead to 10-7, Louisville reeled off 21 straight points in the second quarter to take a 31-7 halftime advantage.
Bilal Powell scored on a 47 yard fake punt run to put UofL ahead 17-7. Powell then caught a 57 yard touchdown pass from Froman for a 24-7 lead. Just before the half, Froman hit Bellamy for a 21 touchdown to put the Cardinals ahead by 24 at the break.
But Arkansas State didn't surrender in the second half.
Aplin directed two third quarter touchdown drives to cut Louisville's lead to 31-21. Aplin connected with Allen Muse for a 15 yard score to make it 31-14, then found Taylor Stickemer for a 24 yard score to make it 31-21 at the end of the third period.
Arkansas State kicker Bobby Zalud made a 35 yard field goal with 8:08 remaining in the game to cut Louisville's margin to 31-24, before Philpott put the game away with his second field goal of the contest with under 4:00 minutes remaining.
Louisville's offense was unstoppable in the first half, racking up nearly 400 yards. The Cardinals finished with 575 yards, including 276 yards on the ground.
Bilal Powell and Victor Anderson both rushed for more than 100 yards, as the Cardinals averaged 5.3 yards per carry in the game.
Powell led Louisville with 21 carries for 156 yards and a score. He also caught two passes for 65 yards and another touchdown. Anderson had his best effort of the season, rushing for 108 yards.
Froman surpassed his season-high 288 passing yards against Oregon State, hitting 20 of 33 pass attempts for 308 yards and three scores.
Froman's favorite target, Josh Bellamy, caught four passes for 66 yards and two scores. Josh Chichester also had four receptions for 66 yards, while redshirt freshman Damion Copeland made three receptions for 61 yards.
Louisville's defense held Ryan Aplin to just 209 passing yards while intercepting the Ark. St. quarterback twice. Aplin entered the contest averaging 299 passing yards per contest.