Just having fun with your code, however, I think this would be cool:

use warnings;
use strict;

my $N = -3;
my $new = "NEW";

while (<DATA>) {
    local $[ = 1;
    my @words = split /\s+/;
    $words[$N] = $new if @words >= abs($N);
    print join " ", @words, "\n";
}

__DATA__
hi there everyone I am looking to substitute
lots of words for new ones, but only the third
word per line on each line!
one
one two
one two three
one two three four

__END__
outputs:
hi there everyone I am NEW to substitute
lots of words for new ones, but NEW the third
word per line NEW each line!
one
one two
NEW two three
one NEW three four
[download]

Yay! Now we can specify from either end :)

Anonymously yours,
Anonymous Monk