The Lions battled hard in the first half and nearly had the opportunity to tie the game up heading into the half, but the Steers forced a fumble on the one-yard line to keep the Lions from getting in the endzone.
The first half ended with a narrow 21-13 lead for Graham.
When play resumed after halftime, the Steers increased their lead with two defensive stops and two quick touchcowns.
Ben Davis would throw all seven of the Steers touchdowns, setting the school record for touchdowns in a game.
Bryce Reeves caught three of those touchdowns and Cameron Patterson caught two.
Hunter Baca and Conner Smith each caught a touchdown a piece.
Vernon would score once more before the end of the game, but by that time Graham's lead was comfortable.
The Steers will take on the Iowa Park Hawks at 7 p.m. Friday, Oct. 18, at Newton Field.