An unlucky own goal by Samir in the first half followed by one each from Nani and Felipe Anderson after the break ended Udinese's seven-match unbeaten league run and took Lazio's goal tally to 56 from 21 league games.
Lazio moved up to 46 points, seven behind Juventus with leaders Napoli a further point ahead.
The hosts went ahead in the 22nd minute when Sergej Milinkovic-Savic fired a low ball across the face of the goal and Samir, attempting to get the ball first, headed it into his own goal.
Portugal forward Nani tapped in from Felipe Anderson's low cross two minutes after halftime and the Brazilian scored the third himself three minutes from time as he burst past two defenders and curled his shot into the net.
Udinese had penalty appeals for an alleged foul on Jens Stryger turned down when they were 2-0 behind, the referee making the decision without reviewing the incident on the video replay system (VAR).
Nani has been hampered by injury since his move to Lazio and his goal was his third in eight games for them.
(Writing by Brian Homewood, editing by Ed Osmond)
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