The game began in cloudy weather with a temperature of 60 °F before the sun came out in the second half. Southwestern entered the game as the favorites and possessed a potent rushing offense. However, the game remained scoreless throughout the first three quarters and well into the final period. New Mexico threatened to score twice, in the first and in the second quarter, but could not advance beyond their opponent's 16-yard line. Southwestern began the fourth quarter with possession on their own 13-yard line. Pirates tailback R. W. MacGruder completed a pass to fullback R. L. Cooper for 27 yards, and soon afterward, MacGruder rushed 22 yards to the Lobos' 19-yard line. However, New Mexico held firm and recovered the ball on downs, but making no progress themselves, were forced to punt. Cooper then completed a pass to the New Mexico 37-yard line for a first down, and then with seven minutes remaining to play, he connected with MacGruder for the game-winning touchdown. William "Spot" Collins kicked the extra point.
After the game, New Mexico lineman Bill Thompson and Southwestern team captain Spot Collins were named the most outstanding players. New Mexico tied a record set two years earlier by Texas Tech University for the fewest first downs. The 1944 game featured the fewest combined offensive yards at a Sun Bowl game.