Udinese played the last quarter with 10 men and survived a flurry of near misses, including a Mauro Zarate penalty, as they clung on for a win that lifted them into fourth place, the Champions League qualifying-round berth.
Lazio, who replied with a Libor Kozak goal, dropped from fifth to sixth, two points behind their opponents.
With AC Milan having wrapped up the title by drawing 0-0 at AS Roma on Saturday, second-placed Inter Milan's 3-1 win over Fiorentina was academic.
Brescia, 19th in the 20-team table, were relegated after one season back in the top flight as they lost 2-1 at home to Catania and 17th-placed Lecce beat fading Napoli by the same score.
Sampdoria finished the weekend in 18th, in the relegation zone, after losing 2-1 to local rivals Genoa where Mauro Boselli scored the winner in the seventh minute of injury-time shortly after team mate Giandomenico Mesto had been sent off.
The bottom three go down, with Bari already condemned.
Uruguayan Ernesto Chevanton scored an 88th-minute winner for Lecce after his compatriot Edinson Cavani, third-placed Napoli's leading scorer with 26 goals, was sent off.
Napoli's third defeat in four games infuriated club president Aurelio de Laurentiis.
"We're not worthy of representing the blue colours of Napoli," he fumed. "Obviously, we're not mature enough to concentrate and finish the season in style."
With two games left, Milan have 78 points, six more than Inter with Napoli a further four behind.
Even if Inter, champions for the last five seasons, pull level on points with Milan, they would still lose out on their head-to-head record.
Udinese have 62 points, two clear of AS Roma and Lazio, while Juventus, who host Chievo on Monday, are a further four back in seventh.
SANCHEZ INSPIRATION
Alexis Sanchez, back from injury, was involved in both goals as he renewed his excellent partnership with Di Natale and Udinese took advantage of slack defending by Lazio.
The Chilean lobbed the ball over the Udinese rearguard, waiting in vain for the offside flag, and into the path of Di Natale who smashed his effort into the roof of the net in the 35th minute.
Seven minutes later, Sanchez sent fellow Chilean Mauricio Isla away on the right and he squared the ball for Di Natale to sweep home the second from close range, his 28th goal of the campaign.
Lazio came to life after the break and the game turned their way in the 66th minute when they won a penalty for a foul on Tommaso Rocchi by Gabriele Angella, who was sent off.
However, Zarate's weak effort was easily saved by Samir Handanovic.
Lazio continued to pour forward and pulled one back in the 76th minute when Zarate's inswinging cross was side
