Substitute Lautaro Martinez's stunning strike ensured Inter are in pole position to finish as runners-up in Serie A after a 2-0 victory over Napoli.
Atalanta's win earlier on Tuesday dropped the Nerazzurri down to third, but Danilo D'Ambrosio's first-half goal put them on course to move directly behind champions Juventus once again.
Martinez then came off the bench and fired home from range in the 74th minute for just his third goal since January as Inter made it seven games without defeat ahead of Saturday's season-ending clash with Atalanta, who are just one point behind them.
A second straight away defeat for Napoli left them seventh, though their Coppa Italia victory has already assured them of a Europa League place in 2020-21.
It took Inter just 11 minutes to go ahead, D'Ambrosio reaching Cristiano Biraghi's cutback and steering a first-time shot into the net.
Napoli then seized control of proceedings, though, with a passage that began with Lorenzo Insigne flicking Piotr Zielinski's effort just wide with Samir Handanovic rooted to the spot.
Handanovic then made saves from Zielinski and Matteo Politano before an Antonio Candreva deflection diverted an Insigne effort wide when a goal looked certain.
Napoli keeper Alex Meret did his best not to be overshadowed, brilliantly tipping Marcelo Brozovic's effort wide at the end of an entertaining first half.
Momentum was lost after the break and an hour had gone when Eljif Elmas next went close when firing wide.
Biraghi could have wrapped up the three points but he got his effort horribly wrong on the counter, and it was left for Martinez to run forward and pick out the bottom corner from 30 yards out to seal it.
What does it mean? Unbeaten run goes on for Conte's men
A second-placed finish in Serie A would be nice but Conte would mainly like to keep this momentum going ahead of the Europa League resumption.
Atalanta, unbeaten since January, will represent a serious test, but Martinez started on the bench here and should be fresh for that, and imbued with the confidence of his long-range goal.
Bastoni a solid presence at the back
This was another clean sheet for Inter – their third in a row – and Alessandro Bastoni deserved plenty of credit for his role in that.
He jointly led the team with five clearances and two interceptions, won both of his duels and had a team-high 77 touches to boot.
Milik goes missing
While Bastoni had a big part to play, Arkadiusz Milik was a bit-part player instead.
The forward had only 18 touches despite being on the pitch for 84 minutes and struggled to get involved throughout.
Key Opta Facts
- Inter have scored the most goals (seven) with their first shot of the match in Serie A this season.
- Martínez has scored four goals from outside the box in Serie A this season. The last Inter player to do better in a single top-flight campaign was Zlatan Ibrahimovic (six in 2008-09).
- Only Robin Gosens has delivered most Serie A assists than Biraghi (six) among defenders his season.
- Napoli have not scored in five of their last six away games at San Siro in Serie A (against Milan or Inter).
- Inter have kept the clean sheet in three consecutive Serie A games for their first time since last September.
Inter round off the season at Atalanta before facing Getafe in the Europa League. Napoli's final Serie A game is at home against Lazio.