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Dover suffered their second successive Skrill South defeat after play-off rivals Weston-super-Mare snatched a late winner on Saturday.
Dayle Grubb scored the decisive goal two minutes from time with a 30-yard strike.
Neither side managed a shot on target during the first half, during which Whites were continually caught out by the Weston offside trap.
But the home side broke the deadlock five minutes into the second half when Chris Kinnear Jnr handled Kane Ingram’s cross and Ashley Kington converted the spot kick.
Dover produced a determined response and they drew level on 66 minutes with another penalty.
Weston’s Naby Diallo was adjudged to have handled and Barry Cogan scored from the spot.
Whites then went looking for the winner and Kinnear saw his effort cleared off the line while Weston keeper Lloyd Irish made a superb save from Ricky Modeste, only for Grubb to have the last word.