Buoyed by the news of Roma's draw in Saturday's early kick-off, Luciano Spalletti's side wasted no time in asserting their authority at San Siro, Icardi putting them ahead after just 35 seconds.
The equally impressive Perisic soon got in on the act, slotting home in composed fashion to all but end the game as a contest after just 13 minutes.
More chances followed for a rampant Inter, Perisic and Icardi combining again four minutes into the second half as the latter tucked in his second at the back post.
Both Mohamed Fares and Antonio Candreva struck the woodwork for their respective sides and there was more drama in the closing stages as Verona goalkeeper Nicolas saw red for a foul on Eder.
Stand-in Romulo was however on hand to deny Borja Valero in stoppage time to ensure Verona suffered no further damage, as Inter cruised to a confidence-boosting victory ahead of Wednesday's Milan derby.
1 - #Inter found their fastest goal in the current league (Icardi after only 35 seconds): the Nerazzurri have scored a goal in first minute of play for the first time since February 2007 (Adriano vs Chievo). Flash. #InterVerona— OptaPaolo (@OptaPaolo) March 31, 2018
Any hopes Verona harboured of causing an upset were dealt a blow with the first attack of the game, Perisic's throw-in carving open their defence, with Icardi alert to sweep home.
Verona could have been two down inside 10 minutes as both Danilo D'Ambrosio and Gagliardini passed up presentable chances, but Inter did not have to wait long for their second.
Having claimed his first assist of the game, Perisic turned scorer as he rushed in behind the visiting defence before squeezing a neat finish in off the inside of the left-hand upright.
Inter had the ball in the net again prior to the half-hour mark – Icardi teeing up Cancelo for what would have been his first Serie A goal – but the strike was correctly disallowed for offside, before Gagliardini headed over at the culmination of an excellent move.
Verona came out for the second half with renewed vigour, but quickly suffered a fresh setback.
Soon after squandering a chance to double his tally, Perisic delivered a wonderful cross to the back post, where Icardi was on hand to prod in a finish.
24 - Mauro #Icardi is the only third Inter's player to score at least 24 goals in 2 Serie A campaigns in a row after Stefano Nyers (1949-50 & 1950-51) and Giuseppe Meazza (1929-30 & 1930-31). Wonderful. #InterVerona— OptaPaolo (@OptaPaolo) March 31, 2018
Icardi made way to a standing ovation as Spalletti cast an eye to the upcoming clash with Inter's city rivals, though that change did not stem the hosts' attacking prowess as Candreva flashed a strike across the face of goal.
Samir Handanovic was beaten when Fares' effort clattered away off the upright, while Candreva curled a strike against the post at the other end.
Verona's day went from bad to worse when Nicolas was sent off for a foul on Eder late on, but midfielder Romulo made a fine save from Valero to deny Inter a fourth.