Bill Lynch improved to 4-0 in home openers as the Hoosiers coach.
Indiana (1-0) scored 38 points in a wild first half that included three touchdown drives of two plays and Willis rushing for more than 100 yards. The Hoosiers also forced two turnovers and blocked a punt in the first 30 minutes.
For the Hoosiers (1-0), things couldn't have gone any better in the season opener.
Towson (0-1), a Football Championship Subdivision school, is now 0-3 all-time against BCS schools.
And this one wasn't even close.
Willis finished with 14 carries for 102 yards, an average of 7.3 yards per carry, and the two scores. Chappell was 16-of-23 for 182 yards and the two scores and the first-half point total was the most produced by Indiana since a 42-point effort against Northwestern in November 2001.
The Hoosiers did it without their top receiver, Tandon Doss, who missed the game with a groin injury.
Indiana's defense was equally efficient. It set up two scores with early interceptions and Matt Ernest, a former receiver, capped the night with a 56-yard interception return for a score in his first college start at cornerback.
Special teams got involved, too. The Hoosiers recovered an onside kick early in the second quarter to set up one score, and Kevin Bush, a 25-year-old Army veteran, blocked a punt late in the first half to set up another.
Not surprisingly, the Hoosiers produced their third lopsided home-opening win in four years.
Tigers quarterback Chris Hart ran 16 times for 123 yards and was 16 of 35 for 165 yards with two TDs and three interceptions. Hart's rushing total was a school record for a quarterback.
But this one wasn't even close.
Tyler Replogle picked off Hart's second pass of the game, and five plays later, Chappell hooked up with Ted Bolser for a 12-yard score.
Mitchell Evans, Indiana's other receiver-turned-defender, picked off Hart on the next series, and two plays after that, Willis finished his 49-yard TD run with a spinning, backward dive just inside the pylon.
After Nick Freeland's 24-yard field goal made it 17-0, the Tigers finally started moving.
Towson converted twice on fourth down on its next drive, the second coming on Hart's zigzagging 42-yard scramble. Hart's long run set up a 5-yard TD pass from Hart to Tom Ryan.
The Tigers then tried an onside kick, which Indiana recovered, and Chappell made Towson pay by hooking up with Damarlo Belcher on a 41-yard TD pass.
Hart answered that with a 64-yard TD pass to Hakeem Moore with 10:16 left in the half, but that was all the Tigers could muster.
Indiana closed the half with a 12-yard TD run from Trea Burgess and Willis' second score, a 2-yard run after the blocked punt.