The Foxes took an early lead when Lloyd Dyer netted, but Leyton Orient came storming back and levelled through Adam Chambers.
The home side then dominated before Leicester caught them out with two late sucker punches.
In a pulsating first half it was the visitors who started well and in the fourth minute Orient's keeper Glenn Morris touched Fryatt's effort against the bar.
But it was the visitors who drew first blood when Dyer raced on to Steven Howard's defence-splitting ball and calmly beat Morris from 15 yards.
Orient responded when top scorer Adam Boyd sent a snapshot wide, but Leicester might have gone further ahead when Fryatt shot over following Max-Alain Gradel's cross from the right.
But Orient gradually forced their way back into the game and after Chambers was twice denied by Leicester keeper David Martin, Orient levelled just before the break.
Jason Demetriou's corner on the left was intelligently cut back by JJ Melligan and Chambers drove the ball home from eight yards.
After the break Orient continued where they had left off and Chambers set Boyd up after a good run but the O's striker shot wide.
Leicester were forced to play on the break, but almost went ahead when Fryatt latched on to a long kick from keeper Martin but the livewire striker lobbed the ball onto the bar.
Ryan Jarvis almost put O's ahead 11 minutes from time but was denied by Martin's smart stop and then came the sting in the tail.
With two minutes remaining Fryatt scrambled Leicester ahead from close range and then, in stoppage time, Fryatt turned provider and set up King to curl home an excellent third to seal the points.