This solution doesn't optimize for minimizing work inside the sort routine, but I think it does optimize for clarity and generality (it would be easy to substitute <=> for cmp, for example):

use Test::More tests => 1;

my @unsorted = (
  [ 'blah', 'asdf', 'foo', 'bar' ],
  ['two'], [ 'zzz', 'def', 'ghi' ],
  ['one'],
  [ 'mmm', 'def', 'ghi' ],
  [ 'qqq', 'xyz', 'aaa' ]
);

my @wanted = (
  ['one'], ['two'],
  [ 'qqq', 'xyz', 'aaa' ],
  [ 'mmm', 'def', 'ghi' ],
  [ 'zzz', 'def', 'ghi' ],
  [ 'blah', 'asdf', 'foo', 'bar' ]
);

my @sorted = sort {
     @$a <=> @$b
  || do {
       my ( $left, $right ) = ( [@$a], [@$b] );
       my $res = 0;
       $res = pop(@$left) cmp pop(@$right) while @$left && !$res;
       $res;
     };
} @unsorted;

diag "@{$_}\n" for @sorted;

is_deeply( \@sorted, \@wanted, 'Sorted array matches expectation.' );
[download]

Output.........

1..1
# one
# two
# qqq xyz aaa
# mmm def ghi
# zzz def ghi
# blah asdf foo bar
ok 1 - Sorted array matches expectation.
[download]

Update: Here's a version that doesn't waste time making copies of the elements for the purpose of pop:

use Test::More tests => 1;

my @unsorted = (
  [ 'blah', 'asdf', 'foo', 'bar' ],
  ['two'], [ 'zzz', 'def', 'ghi' ],
  ['one'],
  [ 'mmm', 'def', 'ghi' ],
  [ 'qqq', 'xyz', 'aaa' ]
);

my @wanted = (
  ['one'], ['two'],
  [ 'qqq', 'xyz', 'aaa' ],
  [ 'mmm', 'def', 'ghi' ],
  [ 'zzz', 'def', 'ghi' ],
  [ 'blah', 'asdf', 'foo', 'bar' ]
);

my @sorted = sort {
  my $res;
  @$a <=> @$b ||
  do { $res = $a->[$_] cmp $b->[$_] and return $res for reverse 0 .. $
+#{$a} };
} @unsorted;

diag "@{$_}\n" for @sorted;

is_deeply( \@sorted, \@wanted, 'Sorted array matches expectation.' );
[download]

Same output as above.