The U's got their first real sight of goal on Saturday when a Damian Batt long throw was nodded back by Luke Foster, James Constable almost reaching the ball ahead of the keeper.
And when Constable knocked the ball forward after a clever dinked pass by Simon Clist, Green raced into the penalty area and went down after slight contact by Terrell Forbes, but the ref adjudged that Green had lost his footing.
Oxford kept Yeovil pegged back in their own half, and it came as no surprise when Midson put the home side in front 10 minutes after the break.
Yeovil had a spell of pressure with Forbes shinning a far-post effort wide and Shaun MacDonald having a shot saved. And Jon Obika had another long-range shot saved in injury-time as the non-League side held out.