I can't find anything in the specification how to do this.
Also I noticed that the implementation in current browsers seem to vary quite a bit (click vs dbl-click, arrow-key's, full versus filtered list and how filters match the partial input, etc).
To me, it seems that for now there is still no properly working combo-box and the data-list seems to be in it's infancy.
So it appears you'd currently be better of to roll your own or use a ready library.
It seems to me the 'minimul datalist' library is rather popular (good link to read to).
On that page is a link to it's GitHub code and a demo page.
Side-note: I'd love that some-one gives a better answer! Also, at first I thought it was a good idea to leave out the arrow-button so people could have better styling-options for a drop-down button if they wanted one that they could hook-up to the datalist/autocomplete/combobox. I'm surprised all this still seems unspecified and not natively supported. Please, spec-writers, give us the simple native combo-box (that is overdue for so long) and then add spice like filters!
Edit: There is an open Feature request since August 2012 on the Chromium project that asks for a drop-down functionality:
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