Superb Di Natale scissor-kick sinks Lazio
The 35-year-old striker met Gabriel Silva's floated cross with a perfectly timed mid-air volley that flew past befuddled Lazio keeper Federico Marchetti in the 19th minute.
The Udinese captain's 18th league goal of the season was enough to lift his side above Inter Milan and Lazio into sixth place, level on 51 points with fifth-placed AS Roma and seventh-placed Lazio.
"We can say that we're on track for the Europa League. We've got Cagliari next and we have to make sure that we win that," Udinese's 18-year-old midfielder Piotr Zielinski, who impressed in his first start in front of home fans, said.
"It's very important for me that I played well with Toto [Di Natale] and he scored," added the Pole, who was given warm applause from the Stadio Friuli crowd when he was substituted five minutes from time.
In the day's only other Serie A game, Genoa missed the chance to move out of the relegation zone with a 1-1 draw at home to Atalanta.
Antonio Floro Flores' first league goal of the season in his first start after three months out injured gave Genoa a sixth-minute lead, only for it to be cancelled out two minutes later by a brilliant Cristiano Del Grosso strike.
It was good work from Gabriel Silva that led to Di Natale's winner against Lazio as he played a smart one-two before floating a perfect cross to the striker, who contorted his body expertly to meet the ball with a volley.
The goal was harsh on Lazio, who had enjoyed the best of the early action and were on the front foot for much of the first half.
Di Natale nearly turned provider just after the hour mark when he played a superb one-two with Zielinski, sending him clean through on goal only to see the teenager shoot straight at Marchetti.
With time running out and a stale second-half display harming their chances of European football, Lazio manager Vladimir Petkovic sent on Hernanes, Ederson and Sergio Floccari in search of an equaliser.
But it was Udinese who nearly doubled their lead with 15 minutes left, Di Natale linking up well again with Zielinski, only for Lazio defender Michael Ciani to pinch the ball from his toes just as his second of the night looked a certainty.
Lazio continued to press for a leveller but could not create any chances and Udinese held out for a win that keeps them firmly in the hunt for Europe.