lower level approaches:

system and qx// are synchronous and make perl wait until the syscall in question is done. You could try system("cmd&") to have the shell run the command and return to perl w/o waiting.

An interesting question now is whether you want $? or the output of the command before finishing to send the page to the client. If that's the case: check out e.g. waitpid, perlipc and maybe also use something like the following sketch

if (not fork()) {system("cmd >cmd-out"); ... exit}
...additionalprocessing-in-parallel...; 
wait; # or a more specific waitpid...;
      # if you've a lot of forks and/or run a long time,
      # consider to reap your children: wait, SIG{CHLD}
      # -> man perlipc
open(FH,"<cmd-out");...
...process the results of cmd and add them to the page...
# (or consider a state file/sessions, if the background
#  command can and should run for more than the duration
#  of a single client request)
finish the page
[download]