If your other program can read STDIN and write to STDOUT, you can construct a data pump by forking twice (this particular code is from memory and therefore untested, but it's something like this):

defined(my $kid = open RESULT, "-|") or die "fork: $!";
unless ($kid) { # kid does:
  defined(my $grandkid = open PUMP, "-|") or die "child fork: $!";
  unless ($grandkid) { # grandkid does:
    print @LotsOfDataHere;
    exit 0;
  }
  open STDIN, "<&PUMP" or die "Cannot dup PUMP to STDIN: $!";
  exec "anotherprogram";
  die "exec anotherprogram: $!";
}
while (<RESULT>) {
 # process the large result
 ...
}
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This is effectively setting up the pipeline of "some_perl_widget | anotherprogram | your_program", but from within the program itself.