They were reduced to 10 men before the break when Ainsley Maitland-Niles was shown a second yellow card for a challenge on James Maddison.
A James Maddison cross was perfectly placed for Youri Tielemans to power a header into the bottom-right corner of the Gunners’ net.
Jamie Vardy made the points safe when he nodded home late on the earn the Foxes a deserved victory before adding another in stoppage time.
Here’s five talking points from the game:
This was a third successive Premier League loss for the out of form Gunners.
It means they remain outside the top four with just two Premier League games left at home to Brighton and away to Burnley .
And it looks increasingly as if their best chance of being in the Champions League next season will be if they win the Europa League where they are into the semi-finals against Valencia.
Boss Emery at least has a proven track record in that competition after winning in three successive seasons with Sevilla.
The Arsenal right-back, 21, must use this game as a big reference point for his development.
He is a promising homegrown defender with 33 Premier League appearances to his name.
But his 36th-minute sending off at the King Power was needless , naive and costly.
First he went in the book for fouling left-back Ben Chilwell.
Then he was guilty of losing possession with a bad touch and lunging in on James Maddison, who made a meal of the tackle to provoke a second yellow.
Boss Brendan Rodgers admitted this week Leicester could break their current transfer record of £29million this summer.
And if it is to land Youri Tielemans permanently from Monaco then it will be worth it.
Belgium midfielder Tielemans,21, has excelled at the King Power Stadium since a January loan switch for Adrien Silva, who went the other way.
A deal to buy the youngster permanently would cost £40m.
But all the evidence suggests he would be worth the massive investment.
Against Arsenal he was pushed higher up the pitch into a more central role where he excelled and opened the scoring after the break with a fine header.
It was his third Premier League goal to add to four assists in England and he also went close from distance.