Palacio's compatriot Ricardo Alvarez completed the scoring in stoppage time at the end of the game.
Inter have scored 27 Serie A goals this season. Twenty-three have come from their South American contingent, Japanese midfielder Yuto Nagatomo has netted twice and one came from Algerian Saphir Taider.
Domenico Berardi grabbed a hat-trick, including two penalties, to give Sassuolo a 4-3 win at Sampdoria while Lazio's problems continued with a shock 2-0 home defeat by Genoa.
Inter are fourth with 22 points from 11 games. They are six points behind Napoli and Juventus, and ahead of Hellas Verona, who beat Cagliari 2-1, on goal difference.
(Reporting by Brian Homewood; editing by Tony Jimenez)
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