The La Liga side, who lie fourth in the standings and who have qualified for the last 16 of the Champions League in their maiden campaign, had one eye on Saturday's league visit of Real Madrid and fielded a weakened side.
They fell behind on a heavy, muddy pitch in the Basque country when Txema Anibarro netted in the 73rd minute following a free kick.
Eibar, who knocked out last year's finalists Athletic Bilbao 1-1 on the away goals rule in the last round, came unstuck in time added on when United States international Onyewu made the most of some poor goalkeeping to head in.
The return leg is at the Rosaleda next month.
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