Luciano Spalletti's side would have secured a place in Europe's elite competition for next season, but they were outclassed by Napoli and go into the final game of the season knowing they could be beaten to fourth by bitter rivals AC Milan.
The visitors offered precious little going forward in the first half and it was no surprise Napoli led at the break, with Piotr Zielinski's stunning 16th-minute strike putting them in front.
Inter failed to stir into life and Dries Mertens' header was added to by a Fabian brace to seal a convincing win in the final 30 minutes, meaning a nervous final match awaits for the Nerazzurri despite Mauro Icardi's late penalty.
Napoli were on the front foot right from the start and deservedly went ahead when Zielinski punished a sloppy Kwadwo Asamoah error by drilling an unstoppable strike into the top-left corner from 30 yards.
Spalletti introduced Icardi for Matteo Politano at half-time, but the Argentinainternational struggled to have an impact and Napoli made it 2-0 in the 61st minute – Mertens nodding Jose Callejon's cross beyond Samir Handanovic.
Kalidou Koulibaly incredibly got back in time to head a Lautaro Martinez effort off the line in the 68th minute and Napoli capitalised soon after, Fabian collecting Mertens' cut-back and firing home.
Fabian doubled his tally 12 minutes from the end when surging into the box and blasting in from a tight angle, before Icardi netted a late consolation from the spot after Koulibaly clumsily tripped him.
Inter with it all to do on the last day
While Inter can console themselves with the fact their fate is very much in their hands, struggling Empoli – who have won three in a row – will not go to San Siro and lie down, knowing they need to secure their top-flight status.
Milan are just a point behind them and in better form. It promises to be an intriguing conclusion to the season.
Fabulous Fabian
Boosted by his recent Spain call-up, Fabian hardly put a foot wrong. The midfielder made four key passes – including the assist for Zielinski's opener – before providing two well-taken finishes to get himself a brace. Inter simply could not handle him.
