Arsenal exuded quality in the first half and took the lead 23 minutes in. Jesus received the ball on the left of the penalty area from Granit Xhaka and curled an audacious lobbed effort over Danny Ward into the far corner.
Jesus, 25, impressed in preseason, netting seven goals in five matches. He extended his goalscoring run by doubling Arsenal's lead 12 minutes after his opener -- heading home at the back post from close range after Gabriel Martinelli's corner was flicked on by Jamie Vardy.
"I am so happy because we played so good against a tough opponent," Jesus said. "I work all day every day to score goals. I was not unhappy at Manchester City, I just wanted to play and the club understood."
Soon after, Leicester were awarded a penalty, but the decision was overturned after a VAR check which adjudged Vardy to have gone to ground too easily.
Arsenal momentarily lost their comfortable advantage early in the second half as William Saliba headed into his own net, but two minutes later Xhaka pounced on a mistake between Wesley Fofana and goalkeeper Ward to restore the two-goal cushion.
James Maddison again closed the gap in the 74th minute as he drilled a shot between Aaron Ramsdale's legs, but Arsenal provided yet another instant response with Martinelli scoring just a minute later after being given space to take aim outside the penalty area.