Has it been more than 24 hours since you booked the $109 ticket? You can cancel an itinerary within 24 hours for a full refund:

http://www.united.com/page/article/0,6722,52184,00.html

If you're within the 24 hour window, I would recommend canceling the $109 ticket, then buying the $64 fare (or vice-versa, buying the $64 fare then canceling the more expensive one).

One thing to consider is that it can be difficult to get a refund, even if you're within the 24 hour window, if you used travel credits or vouchers to buy your ticket.