Quarterback Nathan Scheelhaase threw for a career-best 267 yards. His 16 completions went to Jenkins, who had 11 catches for 148 yards and a touchdown, and Millines, who caught five balls for 119 yards and a score.
Jason Ford rushed for 86 yards and two TDs for Illinois.
The Red Wolves led 8-7 with less than three minutes left in the first half on a safety and a pair of field goals.
But Illinois answered with Millines' touchdown and a field goal before halftime. Jenkins scored his TD early in the third quarter.
Arkansas State quarterback Ryan Aplin was 20 of 32 for 290 yards.