The home side showed their intent within the first minute as Ross McCormack drove a shot at goal which was well saved.
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Dan Burn doubled Fulham's lead with a close-range header on the night that he captained the side for the first time as Fulham dominated the opening period.
Nathan Tyson almost reduced the arrears shortly after the break, but after a mazy run the striker dragged his shot wide of the far post.
With 12 minutes remaining, Doncaster were gifted a penalty after Tim Hoogland's handball, but Bettinelli kept out Theo Robinson's spot kick to ensure the Cottagers recorded their first win under caretaker manager Kit Symons.