Reece Gaines added 18 points for the Cardinals (25-6), who took control with a 10-0 run after applying the press midway through the first half.
Freshman Francisco Garcia went down with an apparent left knee injury late in the first half. But Louisville coach Rick Pitino breathed a big sigh of relief after the star freshman returned in the second half.
"I was just so happy when I heard there was nothing unstable (in the knee)," Pitino said. "I was delighted with that. He's a tremendous player and a big key to our team."
Garcia's status for the second round was uncertain. But that was about the only negative for Pitino, who improved to 8-1 in first-round games and 23-3 when his team plays a lower seed.
"I thought our guys did a great job tonight of staying with Austin Peay's offensive and defensive pressure," said Pitino, who is back in the NCAA Tournament after a five-year absence. "Even when I was in the pros, I loved watching `March Madness.'
"It brings back so many good memories and it's a lot of fun to be a part of again."
Josh Lewis scored 20 points for Austin Peay (23-8), but the rest of the team shot under 36 percent. The Governors struggled throughout from three-point range, missing 13 attempts in a row at one point and finishing two of 21.
"We weren't getting a lot done (from the perimeter)," Austin Peay Coach Dave Loos said. "We have a fairly young team that hasn't been here before. We lost our poise and rushed things a little bit. We didn't get it done inside or on the perimeter."
A pair of free throws by Corey Gipson brought the Governors within 20-19 with 9 1/2 minutes to go in the first half. But Pitino went to the press and Austin Peay reacted poorly, committing three straight turnovers and missing a pair of three-pointers as Louisville pulled away.
"They had the intensity going and we didn't focus," Gipson said. "We just didn't execute. They like to press and really get after it. We didn't go to the post like we should have. We took too many outside shots."
Whitehead and Alhaji Mohammed started the 10-0 run with layups and Mohammed dunked with 8:42 to go before halftime. Whitehead followed his own miss and Kendall Dartez sank a jumper to make it 30-19 with 7:09 left.
Lewis ended Austin Peay's drought from the field at nearly 4 1/2 minutes with a layup. But the Governors could not keep up with the Cardinals, who shot nearly 56 percent in building a 45-33 halftime lead. During the Ohio Valley Conference Tournament, Austin Peay held its three opponents to 36.5 percent shooting.
"We played a good basketball team tonight," Loos said. "Midway through the first half, they really picked up their game. They shot the ball great and we shot the ball very poorly."
Louisville scored 24 points off 18 turnovers and ended a three-game NCAA Tournament losing streak. The Cardinals also had a 44-29 rebounding advantage and won the battle of bench scoring, 28-3.