Luciano Spalletti's men were hoping to take full advantage of Napoli's slip-up at home to Juventus on Saturday and did so in style, cruising to a third successive league victory.
Although the home side wasted several good chances early on, they never looked back after taking the lead through Perisic's 23rd-minute strike.
Mauro Icardi effectively put the game beyond Chievo with a powerful finish seven minutes before half-time, taking his tally to 16 in 15 league appearances this season.
The hosts were far from done, however, with a quick-fire double early in the second half giving the scoreline a rather more impressive look, Perisic and Milan Skriniar getting the goals.
Perisic completed the rout, and his treble, with a left-footed finish late on as Inter moved on to 39 points, one clear of Napoli.
Inter looked every inch a side determined to put themselves top of the table, attacking Chievo relentlessly from the outset.
They went close twice inside the first six minutes, with Andrea Ranocchia – playing in Serie A for the first time since mid-September – heading just over, before Antonio Candreva forced Stefano Sorrentino into a save from a tight angle.
But Inter's dominance paid off midway through the first half – Perisic blasting home on the rebound after Sorrentino had parried a Davide Santon effort into his path.
It should have been 2-0 soon after, but Joao Mario failed to finish after being fed in the area by Icardi on the break.
They did double their lead just before half-time, though, as Icardi raced on to Marcelo Brozovic's through pass and found the net from an acute angle, with Sorrentino likely to be disappointed after getting a touch to it.
Little changed in terms of the flow of the match after the break and Inter got their third just before the hour mark, Perisic pouncing on a poor pass and then drilling a left-footed effort across Sorrentino and into the bottom-right corner.
And they scored another with their very next attack.
Brozovic released Candreva with a wonderful pass up the right flank and the wing-back picked out Skriniar with an inch-perfect cross for an easy headed finish.
Inter looked eager to score as many goals as possible and crafted another couple of chances in the final 10 minutes, with Perisic and Brozovic both going close from long range.
And they did eventually add further gloss to the scoreline with a fifth, as Perisic dragged a left-footed effort into the bottom-right corner from the edge of the box to complete his hat-trick in stoppage time and wrap up a brilliant win.
