The visitors were reduced to 10 men in the first half when Ainsley Maitland-Niles was handed two yellow cards, and Leicester capitalised after the break through a Youri Tielemans header and a late double from Jamie Vardy.
Arsenal have now suffered three straight defeats in the Premier League, and it has left their hopes of achieving a top-four spot at the end of the season out of their hands.
Leicester wasted little time in going on the front foot at the King Power Stadium, and Jonny Evans should have perhaps done better with a header from near the penalty spot after being found by a deep free kick.
Leicester went back on the offensive with Maddison seeing a low effort from an acute angle well kept out by Bernd Leno, before the goalkeeper managed to claw Wilfred Ndidi's header away from the top corner shortly afterwards.
Vardy then fired over the crossbar after latching onto a ball over the top of the backline, but Arsenal responded with Pierre-Emerick Aubameyang playing the ball into the path of Iwobi, who had a low effort kept out by Kasper Schmeichel.
However, the visitors were handed a huge blow with nine minutes of the first half remaining. Maitland-Niles made a mistake on the halfway line, and the right-back reacted by tripping Maddison to leave the referee with little option but to hand him his second yellow card.
Leicester sensed that an opening goal was not too far away, but Arsenal managed to reach half time on level terms with Leno keeping out Vardy's strike at his near post.
Emery introduced Laurent Koscielny before the restart, but the presence of the experienced Frenchman did little to prevent Leicester from keeping Arsenal penned in their own half.
The Foxes continued to build momentum before finally taking the lead before the hour mark, with Tielemans meeting a cross from Maddison to power a header into the bottom corner from 12 yards out.
Arsenal were showing very little at the other end of the pitch, and it only encouraged Leicester to press forward in search of what would almost certainly be a match-clinching second.
Arsenal attempted to find an unlikely equaliser during the closing stages, but the North London outfit's defences were undone for a second time as Vardy finally got himself on the scoresheet.
A long ball from Schmeichel led to Vardy sending a lob over Leno and onto the top of the crossbar, but the striker reacted fastest to head the rebound past Sokratis Papastathopoulos, who had got back on the line.
Vardy soon added Leicester's third in the final seconds of the contest, with the long-serving Foxes man tapping home from close range after getting on the end of Pereira's low cross.
Leicester will now travel to Manchester City with the belief that they can cause an upset at the Etihad Stadium, but Arsenal head into Thursday's Europa League encounter with Valencia knowing that one more bad result may contribute to them having little to show from an exhausting campaign.
LEICESTER CITY (4-3-3): Schmeichel; Pereira, Evans, Maguire, Chilwell; Choudhury (Mendy 79'), Ndidi (Barnes 46'), Tielemans; Albrighton (Gray 86'), Maddison, Vardy
ARSENAL (4-4-2): Leno; Maitland-Niles, Mustafi, Sokratis, Kolasinac; Mkhitaryan (Guendouzi 73'), Torreira, Xhaka, Iwobi (Koscielny 46'); Aubameyang; Lacazette (Nketiah 79')