You can call one program from another and capture its output like this:

my $output = `/foo/bar.cgi`;
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Although that isn't actually calling it as a CGI script. I suppose to do that you could use LWP::Simple and actually make an HTTP request to the CGI script to get the output:

use LWP::Simple;
my $content = get 'http://www.perl.com/';

# manipulate HTML page in $content
# ...

print $content;
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However, I'm not sure that this isn't a situation where you might want to rethink what you're doing... in other words, perhaps you can combine the functionality of these two CGI scripts so that you don't have to call one from the other, particularly since either of the above solutions would be a performance hit.