"Without using references"? By using two-dimensional arrays, you are already using references; two-dimensional arrays are actually arrays of arrays. See perlref, perldsc, perllol.
What you are looking for, I think, is the anonymous arrayref generator, which is a set of square brackets with a list inside, evaluating to a reference to a new anonymous array, contents being that list. Then you assign the reference to one of the elements of the "topmost" array. So, for example:
$two = [ @one ];
will cause element 4 of @two (the two-dimensional array) to contain a reference to an anonymous array initialized from @one (a one-dimensional array), thus assigning @one to row 4 (counting from 0, assuming the indexing goes row, column). Again, see perlref, perldsc, perllol.