Matteo Politano's free-kick and Domenico Berardi's wonder strike left Inter's Champions League aspirations hanging by a thread after they fell to a 2-1 home defeat against Sassuolo.
Luciano Spalletti's men were left to rue their profligacy in front of goal as Giuseppe Iachini's side secured a domestic double over the Nerazzurri, whose top-four hopes may have taken a potentially fatal blow.
Politano's 25th-minute free-kick left the hosts stunned and Berardi's brilliant top-corner finish looked to have put the game to bed in the second half.
Rafinha's well-taken strike 11 minutes from time set up a frantic finish from the hosts as they desperately tried to salvage an equaliser at San Siro, but Sassuolo held out for the win.
Inter now rely on rivals Lazio, who are two points ahead with a game in hand, failing to defeat already-relegated Crotone on Sunday to keep their chances alive.
The pair then meet on the final weekend in a match where Inter will hope they can still seal a return to Europe's premier club competition for the first time since 2012.
The hosts started with plenty of intent but, aside from Marcelo Brozovic's left-footed strike from outside the penalty area, Inter seldom troubled the opposition.
Sassuolo initially defended deep but soon put a stamp on the game and were rewarded in the 25th minute when Politano blindsided Samir Handanovic by slotting a 20-yard free-kick beneath a fragmented Inter defensive wall.
The Nerazzurri sought to recover their early spark and Brozovic saw a close-range strike disallowed for offside three minutes before the break.
Shortly after, Sassuolo goalkeeper Andrea Consigli made a stunning save by diving across goal to deny Mauro Icardi after initially being caught out by Ivan Perisic's cross into the box.
Inter pressed for an equaliser after the interval, with Rafinha twice foiled at close range by Consigli.
But it was the visitors who extended their lead in some style when Berardi collected a pass deep in opposition territory, stepped past Milan Skriniar and curled a beautiful effort into the top-left corner.
That looked to have wrapped things up but, eight minutes later, Rafinha drilled an Ivan Perisic pass through a crowded box with the ball striking the far-right post and nestling in the goal.
It set up a hectic finale where Inter threw everything they had at their opponents, but they were unable to rescue a point and head into next week knowing they need snookers to make the top four.
