Udinese appeared on course for a major upset after Jesper Karlström opened the scoring early in the second half, but Lazio responded through Davide Frattesi and debutant Albert Gudmundsson to secure another narrow victory.
The result means Lazio have now won all three of their Serie A matches, following previous 1-0 victories over Bologna and Genoa. The club's official match report confirmed the 2-1 scoreline and the three goals.
Karlström gives Udinese the lead
The first half ended goalless, with both sides creating opportunities but failing to find the breakthrough.
Udinese eventually broke the deadlock in the 49th minute.
Jesper Karlström finished clinically after Vakoun Bayo provided the assist, sending the ball beyond Lazio goalkeeper Christos Mandas to put the hosts 1-0 ahead.
The goal appeared to put Udinese in a strong position, particularly after they had managed to frustrate Lazio for much of the opening hour.
Frattesi continues scoring run
Lazio, however, refused to panic and gradually increased the pressure.
The visitors eventually found their equaliser in the 75th minute, when Davide Frattesi arrived to convert a cross from Mattia Zaccagni.
It was Frattesi's third Serie A goal of the season, meaning he has now scored in each of Lazio's opening three league matches. His previous goals had proved decisive in the 1-0 victories over Bologna and Genoa.
With momentum firmly shifting towards Lazio, Gennaro Gattuso's side continued searching for the winner.
Gudmundsson seals dramatic comeback
The decisive moment arrived in the 88th minute.
Albert Gudmundsson, introduced from the bench for Frattesi, headed home from a perfectly delivered ball by Danilho Doekhi to complete Lazio's comeback.
The goal was particularly significant for the Iceland international as it came on his Lazio debut.
Udinese were unable to find a late equaliser, leaving Lazio to celebrate a third consecutive league victory.
Lazio move joint-top
The victory lifted Lazio to nine points from three matches, putting them level at the top of Serie A with Roma and Inter Milan. Udinese, meanwhile, remain on four points after three league matches.
For Udinese, the defeat was their first of the season, having opened their campaign with a draw against Como before defeating Monza.
Udinese 1-2 Lazio — Goals
• 1-0 Jesper Karlström — 49'
• 1-1 Davide Frattesi — 75'
• 1-2 Albert Gudmundsson — 88'
Lazio's latest victory under Gennaro Gattuso underlined their impressive early-season consistency. Despite falling behind for the first time in the campaign, the Biancocelesti showed the resilience required to turn the match around and maintain their 100 per cent league record.