Full-time from The Den
The young Lions were made to battle throughout by a gritty Athletic outfit who were finally undone by two goals in five second-half minutes.
Dover started on the front foot and were handed an opportunity to break the deadlock after just six minutes when Green's weak back pass was latched onto by Brandon De Grout, but the visiting No.9 dragged his effort wide of the target with the goal gaping.
The Lions gradually worked their way into the game with Mikael Ndjoli seeing his ninth-minute shot saved low to his left by keeper Tom Roberts and then James White's stinging first-time volley was blocked by a Dover defender.
Ndjoli went close again after 17 minutes, picking up James Brown's throw on the right and surging forward before letting fly with a fierce drive that keeper Roberts pushed around the post for a corner.
Ronnie O'Donnell's subsequent delivery was begging for a Millwall boot to connect with it, but his corner spun across the face of goal as Dover breathed a collective sigh of relief again.
Millwall had a great opportunity to open the scoring after 20 minutes following a sweeping move started by the impressive Chesmain deep in his own half. The left-back sprayed a superb cross-field ball to right-back Brown and the latter's cross landed perfectly in the path of Ndjoli, whose crisp low effort was blocked on the line.
The Lions certainly created enough chances in the opening half to have taken the lead, but Dover defended resolutely and created a half-chance of their own just before the break when Connor Wilkins showed good control to create an opening and then let fly from 18 yards, but contrived to scoop his shot well wide of Ryan Sandford's goal.
David Connolly and Larry McAvoy's young Lions came flying out of the traps after the break with Brown twice testing Roberts in the visiting goal before the keeper produced a top drawer save to tip Alex Mulrooney-Skinner's rasping drive over the bar.
A fabulous piece of play involving Mulrooney-Skinner ended with rampaging right-back Brown's cross kicked clear by the keeper's feet as Millwall kept up the pressure.
Something was going to have to give and on 69 minutes it finally did as The Lions made the all-important breakthrough. Ebere Eze was the provider with a pinpoint free-kick that was met by centre-half Green, who sent a powerful header home.
Ndjoli was denied a second goal on 71 minutes when he burst into the penalty area, took a touch of the ball and hit a low shot that smacked against the bottom of the post with keeper Roberts stranded.
However, Millwall doubled their tally moments later when Chesmain knocked the ball past two defenders, sprinted through the gap before firing home from a near impossible angle and celebrated with a double somersault to the delight of the crowd.
Dover tried to work up a head of steam, but in the end had keeper Roberts to thank for keeping the scoreline down as he first brilliantly tipped James White's bullet header over the bar and then again denied both Ndjoli and Eze as The Lions finished in the ascendency.
Dover Athletic: Roberts, J.Paxman, Dowling, Manning, Connolley, Holmes, Cardwell, Wilkins, De Grout, Carlton, A. Paxman. Subs: H.Miller, Waller, Lightfoot, C.Miller, Walters.
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