Steve Basham hit a hat-trick as Oxford ended any fears of a Cup upset to set up a second round tie at Cheltenham.
Eastbourne started brightly with the influential Yemi Odubade setting up Scott Ramsay to head against the bar.
But Basham opened the scoring after good work by Eric Sabin and made it 2-0 by heading in Chris Hargreaves' cross.
Eastbourne's Andy Atkin and Dean Cox had efforts cleared off the line by Lee Mansell and Leo Roget before Basham completed his hat-trick with a penalty.
Oxford Utd: Turley, Mansell, Willmott, Roget (Stirling 58), Robinson, Hackett, Hargreaves, Quinn, Sabin, Davies (Bradbury 74), Basham.
Subs Not Used: Tardif, E'Beyer, Weedon.
Goals: Basham 20, 45, 90 pen.
Eastbourne Borough: Hook, Austin, Baker, Warner, Tuck (Hemsley 45), Cox, Atkin, Smart (Simmonds 45), Ollie Rowland, Ramsay (Marney 74), Odubade.
Subs Not Used: Piper, Barton.
Booked: Ollie Rowland.
Ref: M Russell (Hertfordshire).