Edoardo Reja's men will have to settle for a place in Europa League next season after missing out on qualification for the continent's elite tournament.
Diego Milito opened the scoring in the first half from the penalty spot, but the Biancocelesti staged a comeback with Libor Kozak, Antonio Candreva and Stefano Mauri netting after the break to help Edoardo Reja's men to the three points.
In the end, however, the result was rendered insignificant as both teams missed out on qualification for next season's Champions League as Udinese defeated Catania to secure third spot in Serie A.
Milito wasted a double chance before he was trusted with the responsibility to take a penalty for a foul on Maicon by Cristian Ledesma in the 45th minute. The Argentine was merciless, skillfully converting from the spot to give the Nerazzurri the lead just before halftime.
Lazio looked rejuvenated after the break, and threw everything forward in search of a comeback against Andrea Stramaccioni's men.
In the 57th minute Ledesma tried to make amends for conceding the penalty, but saw his shot from outside the box saved by Luca Castellazzi. Candreva was next to test the goalkeeper, but he too was denied by the 36-year-old.
Moments before the half-hour mark, Kozak drew the game level by heading in a cross from Ledesma as the Nerazzurri were caught napping. Andrea Stramaccioni's men, however, did not suspect what was in store for them, as in the 63rd minute they conceded another goal.
Lulic went on a marvelous run down the left flank, before finding Candreva near the penalty spot. The 25-year-old controlled the ball before firing home on the volley, leaving Castellazzi helpless.
Inter tried to come back into the game in the remaining minutes of the match, but could only hit the post through substitute Giampaolo Pazzini.
Lazio punished the Nerazzurri's reckless charge in the closing moments of the game through Mauri, who tapped home the clinching goal from close range, but it hardly mattered. Udinese's 2-0 win over Catania meant both clubs missed out on Champions League football.
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