Edouard fashioned several chances to keep the Oxford defence occupied, and put Palace ahead with a well-taken goal in the second-half.
Luka Milivojević added to the forward's opener from the spot in the 90th-minute, guiding Palace into the third round.
Edouard was named Mukuru Man of the Match with 20.8% of the vote, beating Eberechi Eze (13.2%) and Kaden Rodney (11.5%) to first place.
You can see a full breakdown of results below, and find out when the League Cup third round draw is by clicking here.