If your container supports cgi (Tomcat as a standalone has a cgi-servlet) or if you are using a container in conjunction with a webserver that does. You could use sendRedirect to get the user to your perl script.
You could also make a post directly to your perl script (whereever it's running) from your JSP/Servlet app with java.net.URLConnection or with a framework like http://jakarta.apache.org/commons/httpclient. This way you could send Post data to it, and read the results back within your JSP. The end user wouldn't know you were calling a Perl script. This could get pretty complicated if the perl script needs to set cookies, read cgi headers, and or send redirect calls itself.
Another approach would be a shared file or shared database together with either of the above ideas.
No matter how you approach it, it will probably get ugly. What's the Perl script doing that can't be implemented in JSP?