Inter goalkeeper Samir Handanovic made hard saves from Aleksandar Tonev either side of halftime as Crotone, the only team still to score this season, threatened a repeat of April's shock 2-1 win.
Perisic then grabbed his third league goal of the season late on, striking into the far corner as Crotone were caught out on the break, helping secure all three points for Inter.
"We struggled a bit, Handanovic made two important saves but to win like that is a sign of adaptability, mental toughness and great personality".
"It was hot, the pitch was very dry and the wind caused us some problems in the first half", Inter coach Luciano Spalletti said.
"We are not interested in the table right now, we just did what we had to do".
Just a minute later and Handanovic was called into action again.
"We didn't have a great game, but winning was really important".
"It was not easy and our players were very professional, adapting to a style of game they were unaccustomed to", Spalletti told Mediaset Premium.
Second-bottom Crotone have picked up just one point from a possible 12 this season, but started on the front foot and had the best chance of the first half when Aleksandar Tonev's shot from the edge of the box forced a decent save out of visiting goalkeeper Samir Handanovic.
Tonev was again the main threat after the interval and arguably should have scored when sent through on goal and clear of Miranda during the second half, but could only steer his effort straight at the sprawling Handanovic.
Radja Nainggolan had gotten the Romans off the mark after 22 minutes under driving rain, with Patrik Schick making his debut and nearly scoring.
Roma, last season's runners-up, have six points but have played only three games.
Spalletti's previous team AS Roma had to contend with a torrential thunderstorm in the first half as they overcame promoted Verona 3-0, with Edin Dzeko scoring twice after Radja Nainggolan had set them on their way.
Earlier, Fiorentina followed on from last week's 5-0 rout of Verona with a 2-1 win at home against Bologna in a game dubbed the "Apennines Derby" because of the mountain range separating the two cities.
Inter started confidently, but it was the host who enjoyed the first sight of goal after eight minutes.
German Pezzella headed in the victor off a Cristiano Biraghi corner after 69 minutes as the Tuscany side moved up to sixth.
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