Alvaro Gonzalez gave the Rome club the lead in the 17th minute after being set up nicely by Stefano Mauri, who also provided the key pass for Miroslav Klose's goal in the 31st, leaving the German with only the goalkeeper to beat.
Hernanes then put the result beyond doubt in the 59th with a curving free kick over Udinese's wall.
Lazio's Cristian Ledesma had a penalty saved in the 11th and Udinese captain Antonio Di Natale hit the crossbar in the 16th.
Lazio moved within two points of Fiorentina and Inter Milan, which share third, and six points behind Serie A leader Juventus.
Udinese remained five points above the relegation zone.
The top two finishers in Serie A qualify directly for the Champions League, while the third-place finisher enters the final round of playoffs.
Following last week's apparent anti-Semitic attack on Tottenham fans, Lazio players wore shirts featuring the words "NO RACISM" in English across their chests in the space usually reserved for sponsors.
On Monday, Lazio president Claudio Lotito visited a Tottenham supporter still hospitalized with stab wounds from the attack in a downtown pub ahead of a Europa League match.
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