Leicester have 26 points and are above Chelsea on goal difference and one point ahead of champions Manchester City, who visit leaders Liverpool on Sunday.
The Gunners have now gone four games without a win in the league, and the latest defeat will add to the questions being asked of their decision to replace Arsene Wenger with Spaniard Unai Emery.
It was an evenly balanced first half, although Arsenal's looseness in possession frequently handed Leicester opportunities.
This Leicester team have also made a habit of upping their game after the interval, and that was again to be the case against the Gunners.
Arsenal had a 55th-minute effort from Pierre-Emerick Aubameyang ruled out for offside after a VAR review and 13 minutes later Leicester struck.
Vardy produced a characteristic, confident first-time finish from just inside the box after neat passing in the build-up from a confident Leicester side, clearly enjoying their football under Brendan Rodgers.
The goal was Vardy's ninth in 10 appearances against Arsenal and he went close to a second in the 72nd minute but his low drive was kept out by Bernd Leno.
Three minutes later, Vardy turned provider for the Foxes' second, poking the ball back to Maddison whose low strike whistled past Leno.
Rodgers was quick to praise Vardy, the Premier League's top scorer with 11 goals so far this campaign.
"It's firstly about giving him confidence. He is up there with the very, very top strikers in European football with what he brings to a team, his pressing," said the former Liverpool and Celtic manager.
"We've allowed him to do essentially what he wants to do -- how we play, being aggressive and playing quickly obviously suits him. But his finishing ability, how clinical he is, is absolutely phenomenal. That's a big testament to his concentration -- when the opportunities come he's always ready."
Emery said his side had shown better defensive organisation but said he accepted that people will question his work at the club.
"I am speaking with the club to stay strong and recover. We also have young players who are growing up with us," he said.
"I know we are receiving criticism, but I have done before and I have recovered. I accept all the criticism. It is normal. Today we did one step ahead being better defensively," added the Spaniard.
"We need to recover our confidence. We need to be patient with some circumstances, and we are going to do that."