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Dover suffered their third straight home defeat on Saturday when Weston-super-Mare came from behind to snatch all three points at Crabble.
The home side had enough chances to win the game but their visitors from the West Country punished them with a winning goal in the last minute.
Nathan Elder saw two headers fly off target, first from a Craig Stone free-kick and then from an Ashley Carew corner.
At the other end, Naby Diallo's half-volley was well saved by Whites keeper Mitch Walker.
Sean Raggett had a glancing header brilliantly kept out by Luke Purnell in the Weston goal and Richard Orlu then headed against the crossbar.
Dover finally broke through on 59 minutes when Carew's free-kick was not cleared and Ricky Modeste slammed the loose ball home.
But Tristan Plummer scored to bring the visitors level and Diallo then pounced to sink Dover in stoppage-time following a fumble by Walker.
Chris Kinnear's side, 12th in the table with nine points from seven games, are away to Sutton United on Tuesday night.