With two matches to play, Inter have 66 points, one ahead of Atalanta, with AC Milan and AS Roma a further three points back, in the race for a top-four finish and a Champions League place.
Politano broke the deadlock six minutes before halftime with a low shot from the edge of the penalty area which went in off the post.
The visitors, bottom of the table with only two wins all season, battled on bravely but were in more trouble when Nicola Rigoni was sent off for a second booking in the 76th minute.
Inter finally sealed the game when Perisic, who had earlier hit the post, turned in the rebound after a Cedric Soares shot struck the woodwork again.
(Writing by Brian Homewood; Editing by Ken Ferris)
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