nfl overtime rules

Hi guys!

This I think is a great question. It's a question about the most popular sport in the country. One I can not find the answer to anywhere

Ok here it is - In the NFL overtime period if the team who gets the ball first scores a field goal then the other team is allowed an opportunity to march down the field and score either a field goal to tie or a TD to win. Ok, my question is this; What if the team who gets the ball first scores a FG as time expires in the overtime period? Now I realize a 15 minute drive is extremely unlikely, but it is possible (defensive penalties, using up most of the play clock every play, etc.). So What happens? Rules say that their opponent gets an chance to score, but how is that possible if the clock reads 0:00?