MCHS struck first in the upset bid after a first quarter interception by Cody Henson.
David Tadajewski hauled in a fourth down pass from Carter to extend the scoring drive that was capped off by an Austin Reyes one-yard run.
Spring Hill rebounded with two straight scores to take a 14-6 lead before Carter found Jamie Perryman for a touchdown with under two seconds left in the first quarter.
There was no scoring in the second period, sending the two teams to the halftime locker room with Spring Hill leading 14-12.
Marshall County had a chance to take a lead when Spring Hill fumbled the second kick-off, but the visitors got the ball right back on a Tiger fumble deep in Raider territory.
Spring Hill capitalized on the Tiger miscue, marching on a 12-play, 74-yard scoring drive capped by an eight yard TD run by Koderis Ray, making it 21-12.
The touchdown drive motivated the Raider defense, stopping MCHS on a three and out.
The Raiders then put up 14 more unanswered points, stretching the lead to 35-12 over the young Tiger squad.
Carter threw two fourth quarter touchdown passes to Tadajewski from 26 and 61 yards out, respectively.
In between the two Carter to Tadajewski scores, the Raiders found the end zone on a 6-yard run by Nathan Anderson.
The Tigers amassed 321 yards of total offense led by Carter, who completed 14 of 25 passes for 249 yards with three touchdowns and an interception.
Tadajewski grabbed five passes for 138 yards and two touchdowns, while Austin Reyes led MCHS in rushing with 52 yards.
The Raiders finished with 420 yards of offense on the night with Greg Crawford picking up a team-high 82 yards on the ground.
The Tigers (1-7, 1-4) have another tough task this week, traveling to Williamson County to take on the Page Patriots (5-3, 4-1).
Page defeated Fairview 28-18 Friday night at home, notching their third consecutive win.