Froman completed 12 of 16 passes for 235 yards and had touchdown tosses of 39, 48, 4, 28 yards to help the Cardinals build a 35-0 halftime lead in front of 48,427 fans in their homecoming.
Powell, who finished with 18 carries, scored on runs of 74 and 10 yards for Louisville, which begins Big East Conference play next week against Cincinnati.
The Cardinals (3-2) couldn't convert on their first possession of the game against their former Conference USA and Metro Conference rival, but scored on their subsequent five against a team near the bottom of the Football Bowl Subdivision in defensive statistics.
The Tigers (1-5) came in ranked 94th among 120 FBS schools in total defense (408.8 yards per game), and they nearly gave up their average in the first half. The Cardinals compiled 380 yards of total offense in building their five-touchdown lead.
The first shutout victory for first-year Louisville coach Charlie Strong was also the Cardinals' first in four years. Louisville limited Memphis, which entered ranked 110th nationally in total offense and 113th in scoring offense, to just 224 yards of total offense.
Louisville turned Memphis' first -- and only -- turnover into its first points. Cornerback Johnny Patrick picked off a pass by Tigers quarterback Ryan Williams at the Cardinals' 19 and returned it 20 yards. It took Louisville six plays to take the lead it wouldn't relinquish.
The last of those was Froman's first TD pass -- a 39-yarder to Graham.
The Cardinals erupted for 28 second-period points on quick drives of one, six, one and three plays.
Six seconds into the second quarter, on first-and-10 at the Memphis 48, the Cardinals lined up in their "Wild card" formation. Powell took the shotgun snap and handed it off to running back Vic Anderson, who then flipped to Froman. The quarterback, who had lined up as a wide receiver on the play, then found a wide open Chichester in the middle of the field for a 48-yard touchdown.
Froman then sandwiched a pair of touchdown passes of 4 and 28 yards to Bellamy around Powell's 74-yard TD sprint. Powell added another touchdown run, after which Strong pulled most of his starters, early in the third quarter.
Louisville's defense did the rest, holding the Tigers to only 39 rushing yards on 34 carries, in recording the program's first shutout since a 62-0 win at Temple on Sept. 9, 2006.