Kimble had 180 yards passing for the Panthers (4-2, 2-1 Ohio Valley Conference). He also ran for a 9-yard touchdown early in the first quarter. Church finished with 94 yards rushing.
After the Panthers fell behind 34-28 early in the fourth quarter, Kimble capped an 80-yard drive with a 4-yard scoring pass to Church to regain the lead, 35-34, with 9:00 remaining.
Tennessee State ate up the next 5:56 on the ensuing drive but Lane Clark missed a 46-yard field goal try with 3:00 to play and the Panthers held on to win.
Eastern Illinois scored on its first two possessions and led 21-13 at halftime.
Ronald Butler threw for 303 yards and two touchdowns and ran for another score for the Tigers (4-1, 1-1).
No. 1 North Dakota St. tops FCS playoff bracket as CAA gets in record six teams
CAA Football set an FCS playoff record by getting in six teams on the bracket, but North Dakota State's dynasty will be pursuing an even bigger mark in the 24-team field.
Charlotte moving on from Brad Lambert, program's first coach
Charlotte will not retain Brad Lambert after this season, moving on from the only football coach the school has had.
Ohio State's 51-game streak as betting favorite on line vs. Michigan
Ohio State was installed as a 3.5-point underdog against Michigan. Barring dramatic line movement, it would mark the first time the Buckeyes haven't been favored since the inaugural College Football Playoff National Championship in 2015.
The wild Big 12 gets even more fun with Les Miles' return
Even during a tough rebuilding job at Kansas, The Hat will tweak rivals and add entertainment value, just like he did at Oklahoma State in his first head-coaching job.
Breaking down the questions facing Les Miles at Kansas
Can the former LSU coach adapt to the high-powered Big 12? Can he recruit outside talent-rich Louisiana? Welcome to CFB's most interesting new marriage.
Michigan-OSU rivalry produces unforgettable drama
Relive some of the most memorable moments in matchups between Michigan and Ohio State.