Use Linux and clone the disk across.
Short answer: Attach both disks to machine, doesn't matter how, USB or SATA or both is fine.
- Boot Linux (Ubuntu 14.04 look for "Try Ubuntu without Installing")
- Open terminal and identify disks using "sudo fdisk -l" (warning, make sure this is right or you'll destroy your original disk) - for me, /dev/sda was original, /dev/sdd was new.
- Once you *know* you have the right details (double check, this parts dangerous) then clone the disks using "dd if=/dev/oldDrive of=/dev/newDrive".
When done, remove the original disk and install the new disk properly, turn on the machine and you're almost done.
Final step: re-size the partition to use the whole space in the new disk