Justice League Nos. 21 & 22 were published in August & September 1963.
In Crisis on Earth-One the JLA meet the legendary JSA.
 
The two groups team up together in Crisis on Earth-Two to defeat their arch-villains (JLA - Chronos, Dr Alchemy & Felix Faust. JSA - The Fiddler, The Icicle & The Wizard.)  I still remember how curious this story seemed to me when I first stumbled across it in the middle of a Bumper Batcomic Album here as a 6 year old.

Thanks to Mark Cannon for the scan of Mighty #43 the Australian reprint available for only 2/- (two shillings).  Crisis on Earth Two was published down under in All Favourites #45 - thanks to Graeme Fitzgerald for the scan of his copy of this issue.  I'll be keeping an eye out for copies of these two myself!
 

I believe the Spanish language variant cover of JLA 22 was published in Mexico - albeit in a comic headlined by Batman as well!

I've included a smaller scan of the original covers for comparison below.
 

The script was by Gardner Fox and the Art by Mike Sekowsky & Bernard Sachs.
The covers were penciled by Sekowsky and inked by Murphy Anderson.

 
Roll Call
Aquaman, Atom, Batman, Flash, Green Arrow, Green Lantern, Martian Manhunter, Superman & Wonder Woman
 
Atom, Black Canary, Dr. Fate, Flash, Green Lantern, Hawkman & Hourman
 
 Crime Champions
The Fiddler, The Icicle, The Wizard
Chronos, Dr. Alchemy, Felix Faust