Stroud and backup Kyle McCord both threw touchdown passes while completing 12 of their 15 throws.
The Scarlet tacked on another touchdown midway through the second quarter when third-string running back Evan Pryor found a gap on the right side of the line and zipped into the end zone from 22 yards out.
The next drive ended with a 42-yard field goal by Jake Seibert.
The second quarter went much better overall for the Gray, though, as the defense forced a field goal attempt, two punts and recorded a pair of sacks.
The defense forced another punt to start the third quarter, then third-string quarterback Devin Brown led an eight-play scoring drive capped by a 19-yard pass to Reis Stocksdale.
Garrison Smith kicked a 38-yard field goal on the next possession.
The game utilized a scoring system that rewarded the defense for takeaways, sacks, stops and forced punts while the offense scored in the traditional way.
The offense scored on four of the first six possessions before the defense started to do more to hold its own.