As Joost points out, system is the correct way to do this, but there is one caveat. Apparently--see 271092--it's not guaranteed that STDOUT is reopened on file descriptor 1 and STDERR on file descriptor 2. Thus it would be safer to code this way:

open (STDOUT, ">$log_dir/$process.log") or die "cannot open log: $!\n"
+;
if (fileno(STDOUT) != 1) {
  use POSIX;
  POSIX::dup2(fileno(STDOUT), 1) or die "dup2: $!\n";
}
open (STDERR, ">&STDOUT") or exit 2;
flock(STDOUT, LOCK_EX | LOCK_NB) or exit 3;
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