The home side won the spot-kick in the 65th minute after Saphir Sliti Taider fouled Roberto Pereyra in the box, but Di Natale was denied by a fine save by Bologna keeper Gianluca Curci.
The visitors went into the game looking to bounce back from their home loss to Juventus two weeks ago, while Udinese were also short on confidence after a 3-1 defeat at Catania last time out.
The home side started well with Pereyra fashioning a chance from close range in the 14th minute but the impressive Curci got in to block his shot.
And Bologna responded three minutes later by coming close themselves when Panagiotis Kone flashed an effort just over the bar from inside the box.
Curci came to Bologna's rescue again in the 28th minute when Brazilian pair Maicosuel and Gabriel Silva combined before the latter's low shot was deflected onto the post by the keeper.
Curci also saved from Dusan Basta before Udinese's impressive first period came to a close with Andrea Lazzari striking the post from the edge of the box.
Bologna looked better at the start of the second half with Lazaros Christodoupoulos coming close from long range, before Di Natale's spot-kick gave the visitors a reprieve.
Udinese substitute Luis Muriel tried an acrobatic bicycle kick in the 74th minute but the hosts' frustrating afternoon was completed when Di Natale fired high in the box with nine minutes left.