You could try Priceline bidding, but with that you don't have a choice as to time of day. Unless you could leave earlier than evening on the 13th, you'd have to only bid the 14th. Even then you could get a flight later in the day.
If you can live with the risk -
www.priceline.com.
Do watch the final total though, rather than what your initial bid is. Taxes and fees are included in the last step before you actually commit to the bid.