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A wonder goal from Stockport striker Frank Mulhern condemned Dover to their fifth home defeat of the season on Saturday.
The 22-year-old County man fired home from all of 40 yards in the 30th minute after spotting Dover keeper Yusuf Mersin – on his league debut – off his line.
By half-time Dover skipper Kevin Lokko and midfielder Ricky Modeste had both limped off and Whites finished with 10 men after defender Will De Havilland became the third home player forced off by injury nine minutes from time.
The defeat extended their winless run to four National League games and it is now seven since they recorded their only victory at home – 2-1 against Wrexham on August 10.
Dover boss Andy Hessenthaler was forced to make two changes to the side which won at Weymouth in the FA Cup with Jack Munns and Kurtis Cumberbatch coming in for injured duo Joe Bedford and Nassim L’Ghoul.
He also handed former Crawley keeper Mersin his first league start in place of regular No.1 Lee Worgan who was on the bench.
County, unbeaten in their previous two games, made a good start and inside five minutes good interplay between Adam Thomas and Mulhern ended with Sam Minihan drawing a good low save from Mersin.
Dover's first corner led to their first chance on 13 minutes, when Munns hit a low cross which was volleyed wide by Lokko.
That was to prove Lokko's last involvement as the home skipper was helped off the field shortly after, to be replaced by winger Anthony Jeffrey.
Moments later Stockport's fans thought Sam Walker's wickedly dipping shot from 20 yards was in but it just cleared the crossbar.
Modeste whistled a cross-cum-shot across the face of the County goal and Cumberbatch screwed his shot wide from 20 yards, but there was a distinct lack of quality in both final thirds.
That was until the 30th minute when County striker Mulhern saw Mersin off his line and hit a superb dipping shot over him from 40 yards.
Dover responded well forcing several corners, from one which Inih Effiong attempted a lob which was well over.
Bobby-Joe Taylor had a free-kick in the position similar to where he'd scored from in the last home game against Notts County but on this occasion the ball hit the top of the wall and went over.
Five minutes from half-time Stockport could have doubled their lead when Tom Walker was played in but Mersin did well to save with his legs and Sam Walker then had home hearts in mouths when he whistled a drive just wide.
Dover suffered a second injury setback in the dying moments of the half when Modeste limped off to be replaced by Steve Rigg.
The half finished with Effiong blazing over and the second began with the big striker forcing County keeper Ben Hinchcliffe to save from Jeffrey's chipped cross.
As Whites enjoyed a good spell visiting keeper Hinchcliffe was twice called into action, first turning aside Taylor's whipped in free-kick before punching clear from Will De Havilland's downward header following a corner.
Hessenthaler introduced the last of his three subs just before the hour when Roberto Ratti replaced Munns, but the young Italian had little chance to impress.
County defender Festus Arthur forced Mersin to pluck out his header from a Tom Walker corner but the visitors were happy to soak up Dover pressure and break swiftly.
Jai Reason went close on 71 minutes with an angled drive that flew just wide, while at the other end Mersin got down well to deny County sub Nyal Bell.
The Dover keeper also distinguished himself with a great double save to deny Bell and then Osborne on 86 minutes before Taylor cleared Arthur's header off the line.
County's Osborne almost added a second in time added on when his free-kick from 25 yards was inches wide.
Dover: Mersin, Passley, De Havilland, Lokko (Jeffrey 15mins), Rooney, Taylor, Cumberbatch, Munns (Ratti 59min), Reason, Modeste, (Rigg 45mins) Effiong; Subs: Worgan, Simpson.
Stockport: Hinchcliffe, Minihan, Turnball (Keane 84mins), Palmer, Thomas, Sam Walker, Mulhern (Bell 77mins), Arthur, Garratt, Tom Walker, Rodney (Osborne 64mins); Subs: Ormson, Hammill
Attendance: 1154.
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