Cook was able to come back for Michigan State's next drive. He finished 12 of 13 for 285 yards before sitting out the second half.
Michigan State won the Big Ten and the Rose Bowl last year thanks to its outstanding defense, and although that unit lost a few standouts, it was hard to tell the difference against the Gamecocks.
Jacksonville State is considered one of the top teams in the Football Championship Subdivision, but the Spartans showed no vulnerability to an upset in this one.
After his injury scare, Cook threw a 71-yard touchdown pass to Lippett on the first pass of Michigan State's next drive, and a 17-yard strike to AJ Troup made it 21-0.
When the Spartans opened the season last year, they weren't sure who their starting quarterback should be, and the offense was woeful for the first month or so.
Cook grew more comfortable as the season progressed, and now Michigan State is hopeful its offense can take some pressure off that reliable defense.
Next week, the Spartans head west for a marquee nonconference matchup at No. 3 Oregon. That will be quite a test for this Michigan State defense.
Jacksonville State's offense never got untracked. Spartans linebacker Ed Davis provided one highlight in the second quarter when he hurdled a blocker and sacked Eli Jenkins.
Nick Hill ran for two touchdowns in the first half, including a 17-yarder that featured a nice spin past a potential tackler. At one point, Cook was 9 for 9 for 257 yards.
The Spartans led 38-0 at halftime, and when Jacksonville State finally scored early in the third quarter, it was the first touchdown Michigan State had allowed at home since Oct. 12 a span of 215 minutes, 40 seconds.
Lippett had four catches for a career-high 167 yards. Backup quarterback Tyler O'Connor ran for a 3-yard touchdown in the third to make it 45-7.
Jacksonville State's DaMarcus James, who rushed for an Ohio Valley Conference-record 29 touchdowns last year, was held to 17 yards on three carries.