It's absolutely inexplicable why Excel doesn't auto-update an advanced filter once it's created or maybe there's a way to do it I just wasn't able to find but this solution seems to the prevailing one on the interwebz.
Open your VBA editor and drop this code in as attached to the WorkSheet | SelectionChange event. Obviously update it with your own sources, targets and criteria fields.
Private Sub Worksheet_SelectionChange(ByVal Target As Range)
Sheets("Sheet1").Range("A1:C4").AdvancedFilter Action:=xlFilterCopy, _
Hope it helps!