Liverpool suffered an early blow when Bruno Cheyrou was stretchered off with an injury, and was replaced by Vladimir Smicer.
Good work by Smicer, Gerrard and Baros allowed Owen space in the box and he netted from 10 yards out.
Danny Murphy nearly added a second soon after, but his shot fell onto the top netting.
Vitesse started the second half in a better frame of mind and were unlucky not to have equalised with several chances.
Owen had a couple of second half chances, but the Vitesse keeper did well to close him down on both occasions.
On a positive note, Stephane Henchoz played a full 90 minutes after returning to the first team.
Vitesse Arnhem: Jevric, Cornelisse, Stefanovic, Frankel, Mustapha Riga, Claessens, Mbamba, Janssen, Levtsjenko, Amoah, Zeman. Subs: Van Fessem, Van Beukering, Peeters, Dingsdag, Sone, Bochem, Rojer.
Liverpool: Dudek, Babbel, Henchoz, Hyypia, Traore, Murphy, Gerrard, Diao, Cheyrou, Owen, Baros. Subs: Smicer, Heskey, Diouf, Kirkland, Carragher, Biscan, Welsh.
Referee: Mejuto Gonzales (Spain)