The visitors came close to taking the lead early on, but after finding some space on the edge of the box, Giacomo Bonaventura fired wide.
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Midway through the first half the visitors took the lead through Davide Brivio, who was picked out at the back post by Cristian Raimondi, before directing the ball past Simone Scuffet and into the far corner.
After the break Dusan Basta fired wide for the home side, before Di Natale saw an effort saved by Consigli.
In the 71st minute Udinese were given the chance to equalise when Guglielmo Stendardo gave away a penalty for dragging down Di Natale inside the box
Di Natale himself stepped up to take the spot kick and fired the strike into the back of the net, sending Consigli the wrong way.
Luca Cigarini came close to scoring a second for Atalanta in the closing stages when his long-range effort struck the crossbar, but neither side could find a winner and the game finished level.