The LWP idea is bang-on.
My roommate (both of us Computer Science majors) spurned Perl despite my testimonial. But then he wanted to write a script that was right up
WWW::Mechanize's alley, munging some web pages and submitting some forms. He was saying "I want to do this program, but it will be really painful and messy." And I said "I can do it in 30 lines of Perl." Of course he didn't believe me.
So, whether it's LWP or WWW::Mechanize, get them thinking about some problem that would be excrutiating in another language, then show the simplicity of the Perl solution.
It took me 22 lines. He uses Perl a lot now.