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Inter followed Atalanta into the Champions League but their 2-1 win at San Siro on Sunday relegated Empoli.
Mauro Icardi had the power to end the match for Inter Milan. The Argentine striker took a penalty that he himself won but his shot was awful, straight down the middle, making it easy for Dragowski.
Inter will qualify for next season's Champions League if they beat Empoli and Luciano Spalletti is confident they will.
Empoli goalkeeper Bartlomiej Dragowski made 17 saves to keep a clean sheet in a Serie A draw with Atalanta on Monday.
Napoli fell 2-1 to relegation candidates Empoli on Wednesday opening the way for Juventus to claim an eighth consecutive Serie A title from as early as this weekend.
Aurelio Andreazzoli, the Empoli coach, went to the press room at the Juventus Stadium, after his team's match. But there were only two journalists there.
Moise Kean came back from the international break with lots of motivation and the same hunger as usual. The 19 year-old striker came onto the pitch in the 69th minute and three minutes later in the 72nd, he scored to break the deadlock.
Aurelio Andreazzoli has returned as coach of Serie A strugglers Empoli in place of sacked Giuseppe Iachini after just four months after being removed himself, the Italian team confirmed on Wednesday.
Inter Milan travel to Tuscany side Empoli on Saturday without their fans after racism and violence overshadowed Christmas football in the Italian league.
Dries Mertens scored a hat-trick as Napoli warmed up for next week's crucial Champions League game against Paris Saint-Germain with a 5-1 thrashing of Empoli to go back to second place in Serie A and put the pressure on champions Juventus.
Napoli will be looking to hit struggling Empoli hard in Friday's early Serie A match to keep touch with leaders Juventus before next week's Champions League blockbuster against Paris Saint-Germain.