The Tar Heels grabbed a lead they would not relinquish when midfielder Cameron Brown played a ball from midfield over the Indiana defense to Dixon, who split two defenders, settled the ball and sent a six-yard shot under IU keeper Luis Soffner.
The win moves UNC into the quarterfinals against Drake on Friday at Fetzer Field.
"This was not out most beautiful performance for sure," said UNC coach Elmar Bolowich, who has led UNC to five quarterfinal appearances. "In order to advance, we have to do better. We have to do better on Friday. I thought we struggled today with finding our rhythm early. Several players were a little bit off here and there. We couldn't quite connected, and as result, for my liking, Indiana had too much of the play. They are a good side. I don't want to take anything away from them. They are a competitive team and know how to play these games."
Goalkeeper Brooks Haggerty preserved the shutout -- Carolina's third straight shutout since the close of the regular season -- with four saves.
Haggerty turned away Indiana's best scoring chance in the 80th minute when Andy Adlard turned and fired from 10 yards, but the UNC keeper saved the one-on-one chance.
"We knew coming down here it was going to be a tough task against a team that keeps it solid and they don't give things away," said
Indiana head coach Mike Freitag. "But I would also like to congratulate my team on a season where I really challenged them with our schedule and they found a way to get it going at the end of the season to make it to the sweet sixteen. I am awfully proud of them."