The result moved Mikel Arteta's side onto 21 points, mathematically guaranteeing a top-eight finish and extending their run to seven consecutive league phase wins.
Gabriel Jesus was the standout performer, scoring twice in the first half to provide a consistent attacking threat throughout the contest.
The 28-year-old, making just his third start of the season after returning from a cruciate ligament injury that sidelined him for nearly a year, opened the scoring in the 10th minute. He capitalised on a mishit effort from Jurrien Timber to claim his first Champions League goal since November 2023.
Inter, coached by Cristian Chivu, responded by abandoning their cautious approach and drew level in the 18th minute through a long-range strike from Petar Sucic.
The hosts had chances to take the lead, with Sucic missing a clear opportunity after being played through by Lautaro Martinez, while Marcus Thuram fired over following a poor pass from Sucic.
Arsenal regained control four minutes later from a set-piece routine. Bukayo Saka delivered a deep corner, Leandro Trossard headed against the crossbar, and Jesus finished from close range after being left unmarked, with Inter sloppy once again.
"He's an unbelievable player," Arteta said when asked about Jesus.
"The bigger the game is, the more comfortable he plays.
"I'm so happy for him. I think he deserves the man of the match award not only for the goals but for the work that he's done.
"But not just him, many of the players. Otherwise you don't win at San Siro."
Federico Dimarco and substitute Pio Esposito went close for the hosts, but substitute Viktor Gyokeres sealed the win on the counter-attack in the 84th minute.
Despite struggling this season, his goal compounded Inter's misery as they lost three consecutive Champions League matches for the first time in their history.
Arsenal now sit six points clear at the top of the classification, with Bayern Munich second ahead of their match against Union Saint-Gilloise. Inter, eighth in the standings, could yet secure a play-off spot by beating Borussia Dortmund next week.
Chelsea are continuing to grapple with a virus that has disrupted preparations ahead of their upcoming Champions League fixture, with Enzo Fernandez the latest to be affected.
Liverpool head coach Arne Slot has played down recent tensions surrounding Mohamed Salah, insisting the matter is now firmly in the past following the forward's return to Anfield.
Champions league holders Paris Saint-Germain suffered a 2-1 defeat away to Portuguese side Sporting on Tuesday.
Manchester City's difficult run continued with a damaging 3-1 defeat away to Bodo/Glimt in Norway, compounding the disappointment of their loss to Manchester United at the weekend.
