The keys of the hash are what you want to print out. If I understand your difficulty, all you need to do to get your desired result it to use $key in place of $hash{$key} in your print statement, i.e.

#!/usr/bin/perl
use strict; 
use warnings;
my $count = 1;
my @array = ('A','B','C');
my %hash = ();

for my $i (@array) 
{
  # set key AND initialize by $count as value of key.

  $hash{$i} = $count;      
  $count++;
}
for my $key ( sort {$hash{$a} <=> $hash{$b} } keys %hash )
{
     print " MIRACLE_HAPPENS is equal to $key.<br>\n";
}
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