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The visitors were awarded a penalty with 15 minutes gone when Andrea Lazzari was brought down by Michele Pazienza. Veteran striker Di Natale placed the spot kick beyond Gianluca Curci's grasp and into the bottom left corner.
But it was the Bianconeri who continued to look the more likely in attack with former West Ham United striker Alessandro Diamanti posing a threat to the Bologna goal, but he was unable to make the most of his opportunities.
Bologna's best opportunity to get back on terms came midway through the second half when Davide Moscardelli's left-footed shot went just wide of the visitors' goal.
As the second half wore on, Udinese pressed for a second to put the game beyond the hosts, with Di Natale slipping the ball wide of Curci's goal from six yards out.
Dusan Basta then saw his effort from the edge of the box blocked by the Bologna defence as the visitors looked the more likely to score.
Bologna had a chance to score a late equaliser when Robert Acquafresca's header from Lazaros Christodoulopoulos's corner drifted just wide of Brkic's right-hand post.
The win was sealed when Lopez slotted the ball past Brkic in stoppage time to put further daylight between themselves and the relegation zone.