The Magpies survived an early setback when Cameron Congreve fired the visitors into a shock lead at St. James' Park, but Miley's rocket - on his first start of the campaign - levelled matters before the break.
Substitute Gordon put United in front from the penalty spot after the restart before summer signing Osula's first goal for the club wrapped up the victory and sent Eddie Howe's side through and set up a trip to League One leaders Birmingham City in the next round.
Serena Taylor and Michelle Mercer were there to bring newcastleunited.com this gallery from another successful cup outing.