Jordan McGhee and Osman Sow were also on target in the home win which featured a minute’s applause before the game for 14-year-old supporter Robbie McDonald who passed away this week.
Prince Buaben saw red late on for a reckless challenge before Falkirk netted a late consolation through towering striker Botti Bia Bi.
The teams traded early blows as first Buaben went close for Hearts before Blair Alaston saw his effort deflected wide for the visitors.
But on 17 minutes Hearts took the lead when McGhee leapt at the far post to head King’s corner into the top corner of the net.
And things went from bad to worse eight minutes later when Alan Maybury was penalised by referee Kevin Clancy for a foul on Sam Nicholson.
James Keatings saw his penalty brilliantly saved by Jamie MacDonald but King was on hand to put the rebound in the back of the net to double Hearts’ lead.
And King extended the home side’s advantage after 37 minutes when his right-footed effort from inside the area proved too good for MacDonald.
King almost sealed his hat-trick shortly before the break when his shot from outside the area flew inches above the top right corner of the net.
Nicholson and Keatings drew saves from MacDonald as Hearts searched for a fourth but the home side were reduced to 10 men when Buaben was dismissed for a two-footed lunge on Olumide Durojaiye after 71 minutes.
It did not stop the 10 men from going four-up on 78 minutes when Sow stepped up to convert a penalty after being fouled in the area by Will Vaulks.
Bia Bi grabbed a consolation for Falkirk when he fired home late on but another good win for Hearts saw them remain top of the Scottish Championship.