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Dover's winless run in the National League is up to four games after another dramatic late defeat at Crabble.
Mark Beck's early header gave the visitors a lead which they held until 11 minutes from time when Jamie Allen spun superbly in the box to fire home.
Just 90 seconds later the comeback was complete as the ball broke to Jai Reason just outside the box and the midfielder curled a peach into the top corner.
It was no more than Whites deserved after a dominant final half-hour but they were pegged back on 84 minutes when Beck headed his second to tie the game up.
Then, just as the board went up to say there would be four added minutes Harrogate midfielder George Thomson fired into the far corner from fully 30 yards to climax a breathless finish.
Boss Andy Hessenthaler was forced into making one change to the team which had been beaten at home by Gateshead the previous week,
Midfielder Nortei Nortey was ruled out by illness meaning a return to the starting line-up for Bobby Joe Taylor.
Whites were looking for a first win in four but they made the worst possible start falling behind inside seven minutes.
Jack Muldoon hit an excellent crossfield pass to Jack Emmett whose cross to the near post was headed home by Beck, who had missed a penalty in the FA Trophy game between the sides last month.
Jamie Allen shot at James Belshaw from 25 yards early on, but the home side's best route to goal appeared to be through set pieces.
Their best spell came midway through the half when they twice came close to an equaliser.
National League player-of-the-month Kevin Lokko thought he had headed them level on 23 minutes only for his effort to be flagged offside.
Five minutes later Taylor played Reason in but the midfielder's shot was blocked by Belshaw who had raced outside of his area.
Inih Effiong blazed an early second half chance over for Dover but it was the visitors who looked the tidier in possession with Josh Falkingham and Emmett both missing the target with shots.
Dover then began to take a hold of the game and created two great chances in the space of five minutes.
The first came when Allen released Effiong but his shot was blocked at close quarters by Belshaw who then grabbed the rebound.
With 71 minutes played Lokko got up well to meet a set piece and when the ball fell to Pavey at the near post his effort was superbly kept out by Belshaw.
Effiong sent a header wide but the game looked to be drifting away from Whites when Brundle's long throw was helped on by Lokko and Allen produced a smart finish from eight yards.
It was another Brundle throw which led to Dover's second, as Reason precisely curled the ball beyond Belshaw but within two minutes we were all square again as Harrogate sub Aaron Williams crossed to the near post and Beck headed his second.
If that was hard to take for Whites then what followed was even worse as Thomson spectacularly fired home to condemn Dover to their second injury-time defeat in as many weeks. The defeat also dropped them back into the bottom four.
Dover: Walker, McNamara (Modeste 75mins), Doe, Lokko, Debayo (Pavey 64mins), Brundle, Lewis, Taylor, Reason, Effiong, Allen. Subs: Sho Silva, Adebowale, Worgan
Harrogate: Belshaw, Falkingham, Kitching, Senior (Howe 59mins), Fallowfield, Thomson, Beck, Emmett, Burrell, Muldoon (Williams 82mins), Kerry (Mottley-Henry 75mins); Subs: Cracknell, Woods.
Attendance: 997.