Two goals in three minutes midway through the first half from strikers Matt Green and James Constable put Oxford United in charge against Eastbourne at the Kassam Stadium.
The visitors began well and carved out the better openings in the first 20 minutes.
But Green opened the scoring on 25 minutes by firing in low from 12 yards after a good overlapping run by Damian Batt.
And in United's next attack, Constable ran on to Adam Murray's pass and drove low past the keeper.
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