Minus some misformatted delimiters on your my @item_array = ... line in the OP, everything you've posted seems good. Specifically,

#!/usr/bin/perl
use strict;
use warnings;
my @item_array = ([1, 2, 20],
                  [2, 3, 15],
                  [3,4,3],
                  [4, 5, 17],
                  [5,6,28],
                  [6,1,23],
                  [1, 7, 1],
                  [2, 7, 4],
                  [3, 7, 9,],
                  [4, 7, 16],
                  [5, 7, 25],
                  [6, 7, 36],
                  );
my @sorted_array = sort { $a->[2] <=> $b->[2] } @item_array;
for (@sorted_array) {
    print join("\t", @$_), "\n";
}
[download]

Outputs:

1    7    1
3    4    3
2    7    4
3    7    9
2    3    15
4    7    16
4    5    17
1    2    20
6    1    23
5    7    25
5    6    28
6    7    36
[download]

Note I copied/pasted the sort. As well, note that curly brackets are used in hash references, square brackets in array references, and parentheses in list construction. See perlreftut.

Are you sure that your array contains what you think it contains? See How can I visualize my complex data structure?. The short answer is is use Data::Dumper to make sure your array contains what you think it does: use Data::Dumper; print Dumper \@item_array;