Byrd scored with 11:15 to go in the first quarter and added his second touchdown of the night before halftime to lead the Mean Green (1-1) to victory.
North Texas had 497 total yards of offense against the Tigers (1-1), 352 of which came on the ground. Antoinne Jimmerson gave the Mean Green a dual threat from the backfield, recording 15 carries for 139 yards and one score.
The Mean Green was quite efficient from the red zone, scoring six out of seven times, two of which were field goals by Zach Olen from 34 and 28 yards out.
Daniel McKayhan caught three balls for 75 yards and a touchdown for Texas Southern in the loss.