The Biancocelesti condemned the Nerazzurri to a record 15th Serie A defeat in one campaign, ending any hopes of a place in European competition next season for the Milan outfitInter's hopes of competing in European competition were ended as some lackluster defending helped Lazio to a 3-1 win at San Siro.
Andrea Stramaccioni's men began well but were pegged back by a defensive mix-up which saw Samir Handanovic turn into his own net. Ricardo Alvarez equalized for the hosts before Hernanes capped his 100th Serie A appearance with a goal from the penalty spot on the stroke of halftime.
Inter resorted to shooting from range in the second half but none could provide the sort of effort that Ogenyi Onazi did to grab the third for Vladimir Petkovic's men, consigning the hosts to a record 15th league defeat in one season.
In a lively start to proceedings which saw both teams on the attack, the best chance of the early exchanges came in the 10th minute.
Mateo Kovacic wriggled away from a group of Biancocelesti shirts, surged forward and slipped perfectly-weighted through-ball to Tommaso Rocchi who saw his shot beaten away by Federico Marchetti.
The Nerazzurri continued upon their positive start but some shambolic defending saw them fall behind in the 22nd minute.
A lack of communication was evident as Handanovic failed to claim Antonio Candreva's cross, instead deflecting the ball into the back of the net with the help of Andrea Ranocchia.
Candreva could have then added one himself two minutes later as Lazio countered but he dragged his shot wide when one-on-one with the keeper.
Inter fought back and after Handanovic had denied Candreva from an acute angle, the hosts restored parity.
Alvaro Pereira worked enough space on the left to send a cross into the area and Alvarez towered over Lorik Cana to head the ball in off the underside of the crossbar.
There was little Marchetti could have done to stop that effort, but two minutes later he proved his quality with a tremendous save to send Esteban Cambiasso's shot onto the post and behind.
Stramaccioni's men could have added to their tally further before the break but Lazio was gifted the chance to go take an advantage into the break as Ranocchia felled Floccari in the area. Hernanes took responsibility from the spot, stuttering on his run-up before lashing the ball into the corner.
Fredy Guarin had been extremely quiet in the first half but emerged as a different player after the restart, but the Colombian failed to convert from a trio of great chances before the hour mark.
The Nerazzurri ramped up the pressure on their visitors and Guarin's persistence eventually reaped rewards as he drew a foul from Cana inside the area. Alvarez stepped up to take the spot kick but lost his footing as he struck the ball and sent it well off target with 20 minutes.
It took a top save from Handanovic to keep out Hernanes but there was no chance that the Slovenian was going to get anywhere near a thunderous effort from Onazi that arrowed into the top corner with 13 minutes left.
The goal all but ended hopes of a comeback for Inter, which will not feature on the continent next season following Udinese's win over Palermo. Lazio, meanwhile, has every chance of playing European football next term.