How about a do..while() so that the read happens at the end of the loop instead of the beginning:

#!/usr/bin/perl -w
 
use strict;
 
$_=<DATA>;
(my ($first, $second), $_) = split(/\s+/, $_, 3);

print "first: $first\n";
print "second: $second\n";

do{
print "rest: $_";
} while (<DATA>);
 
__DATA__
This is line one!
This is line two!
This is line three!
This is line four!
This is line five!
[download]

Outputs:

first: This
second: is
rest: line one!
rest: This is line two!
rest: This is line three!
rest: This is line four!
rest: This is line five!
[download]

HTH