Inih Effiong’s stunning finish ensured it was honours even on Tuesday night.
Dover’s striker smashed Ricky Modeste’s volleyed pass into the top corner to cancel out an early penalty from the Southern Counties Eastern Football League side as Andy Hessenthaler’s side made it three pre-season matches unbeaten.
Though it was Whites who could have taken the lead from the spot with the game just a couple of minutes old following a foul on a Dover player.
Jai Reason stepped up, but skied his penalty and it was the hosts who took the lead from 12 yards on 11 minutes.
After referee Gerry Heron spotted a handball in the area by a Dover player, Yusuf Mersin was sent the wrong way.
Nassim L’Ghoul and Ricky Modeste both fired narrowly off target for the visitors before Effiong struck in style and Dover went close to having a half-time lead.
Scott Doe headed goalwards, only for the home keeper to spectacularly tip the ball over the bar.
A much changed Athletic side were almost stunned after the break when Beckenham struck the post from 25-yards.
Steven Rigg then saw his accurate header cleared off the line and Alfie Pavey curled inches over when well placed.
Mersin was called into action with injury-time looming, stooping low to keep out the home side as the match ended in a draw.
Dover first half XI: Mersin, Passley, Doe, De Havilland, Taylor, Woods (c), L’Ghoul, Munns, Modeste, Reason, Effiong.
Dover second half XI: Mersin, Passley (Trialist 65), Doe (Trialist 65), Lokko (c), Taylor (Trialist 65), Trialist, Trialist, Cumberbatch, Trialist, Pavey, Rigg.