Stockstill has thrown for more than 300 yards in six games this season and is one shy of tying the school record held by Wes Counts who had seven his entire career.
The Middle Tennessee (5-5, 4-2 Conference USA) defense forced Florida Atlantic to turn the ball over on downs on its last two drives.
Stockstill threw a 62-yard touchdown to Richie James in the third quarter for the go-ahead score with the game knotted at 17. James finished with nine catches for 198 yards and two scores. Stockstill also connected with James for a 69-yard score in the first quarter.
Shane Tucker added 103 yards on 25 carries for the Blue Raiders.
Florida Atlantic (2-8, 2-5) got 214 yards passing from Jacquez Johnson who threw two touchdowns and an interception.