The first half saw a solid performance by Gateshead, who peppered the Eastbourne goal and on another day could have scored four or five.
Non-Veteran Graeme Armstrong bagged two goals in three minutes to give Gateshead a 2-0 lead after 17 minutes.
The first, scored on 14 minutes was set up by Craig Baxter whose cross found the 26 year-old.
Michael Mackay supplied a cross form the left which saw Armstrong loop a ball over Michael Jordan who was left helpless.
Eastbourne came close in the second half as they tested Paul Farman, and had a goal notched off when a header from a corner was seen as a foul by the match officials.
Phil Turnbull put the game out of reach for Eastbourne on 83 minutes as a 15-yard striker found the back of the net after Turnbull was set up by Captain Kris Gate.