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Skipper Kevin Lokko marked his return from injury with a goal but Dover's hunt for a second home win of the season goes on.
Lokko –starting for the first time in five matches – looked to have claimed the points when he struck midway through the second half, only for County substitute Kristian Dennis to head home in the 89th minute.
Bobby-Joe Taylor had opened the scoring with a stunning 35th minute free-kick but went from hero to villain by conceding the penalty from which Mitch Rose equalised soon after.
Dover boss Andy Hessenthaler rang the changes after last week's 2-0 home defeat against Halifax with Lokko, Passley, Jack Munns and Nassim L'Ghoul all coming in.
Aaron Simpson, Michael Woods, Kurtis Cumberbatch and Ricky Modeste were the players to miss out, all but Woods (suspended) on the bench.
The returning Passley almost gave Whites the perfect start, beating County keeper Sam Slocombe to Jai Reason's cross only to see his header clip the crossbar and go over inside two minutes.
Whites started the game very much on the front foot, something they did not do last week against Halifax.
Defender Will de Havilland provided a good example, feeling confident enough to advance forward before dragging a low drive wide.
Inih Effiong spun to hit another effort wide, while at the other end Taylor hared back to make a vital tackle on Wes Thomas.
Thomas then squandered County's first real chance when he blazed over after being teed up by Enzio Boldewijn.
Effiong's teasing cross just eluded the diving Steven Rigg before Whites were given a free-kick in a promising position which Reason curled comfortably over.
County squandered a great chance to go ahead on 27 minutes when Kyle Wootton fired straight at Lee Worgan from the edge of the box and eight minutes later Whites had the breakthrough.
Keeper Slocombe lined-up a four-man wall to defend Taylor's free-kick 20 yards out but the full-back got his angles right by curling a superb left-foot shot into the top corner.
Taylor did not do quite so well four minutes later when he tugged at former Bromley team-mate Richard Brindley as the County man burst into the box.
Referee Alan Dale pointed to the spot and skipper Rose sent Worgan the wrong way to equalise.
Whites should have regained the lead with the last kick of the half but Effiong was blocked at close quarters by Slocombe after Reason's free-kick had fallen favourably for him.
Whites replaced De Havilland with Modeste at half-time but immediately had some defending to do as Worgan saved well from Sam Osborne who then had another effort blocked.
Hessenthaler was forced to make a change on 54 minutes when Rigg limped off injured to be replaced by Cumberbatch.
Three minutes later Whites regained the lead when Lokko turned home from close range after Passley's deep free-kick had dropped favourably to him in the box.
That lead was spectacularly preserved on 65 minutes by Worgan who beat away Wootton's drive before diverting Thomas's point blank follow-up over the bar.
Dover went close to a third goal on 77 minutes when sub Cumberbatch just failed to get decisive contact on Modeste's fizzing cross.
Moments later Effiong was blocked out as he bore down on goal and the big striker burst clear again in the 83rd minute but his lofted effort was well over.
County pressed for an equaliser but Whites looked to have hung on until Rose's chipped cross was headed home from eight yards by sub Dennis.
Cumberbatch might even won it in injury time but County keeper Slocombe got out well to block with his feet.
Whites have now gone six games without winning at home. Their sole success was the 2-1 victory over Wrexham on August 10.
Dover: Worgan, Passley, Taylor, Lokko, De Havilland (Modeste 46mins), Doe, Munns, Reason, L'Ghoul (Jeffrey 73mins), Effiong, Rigg (Cumberbatch 54mins); Subs: Simpson, Mersin.
Notts County: Slocombe,Rose, Turner, Thomas (Dennis 79mins), Boldewijn, Rawlinson, Wootton, Booty, Bakayogo, Brindley, Osborne (Shields, 75mins); Subs: Tyson, Bird, Dunn.
Attendance: 1463
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