There's a bit of lipping it involved (especially across the 12th), but most of the secret is to drop the back of the tongue (usually somewhat arched) to open up the chamber of the mouth/throat and allow you to play with the resonance a bit. You'll usually hear that run with a bit more of a "wah" (I'm pretty sure I remember that being the official, technical term ^_^)to the timbre than is normal for a clarinet, tightening up into a more normal timbre at the top (where, honestly, fingering is mostly wishful thinking, and has less to do with selecting overtones than lipping does).
On a somewhat related note, the advent of MIDI and the subsequent wind-type controllers meant that I'd spent a whole bunch of money on a Lyricon the previous year for nothing...