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Dover's Wembley dream in the FA Trophy remains alive, just after they snatched a last minute draw at home to Guiseley.
Off-colour Whites never got out of second gear and were stung by a entirely preventable
goals either side of half-time.
However a last-minute finish from substitute Duane Ofori-Acheampong ensured a 2-2 draw and a trip to Yorkshire for the replay on Tuesday night. Dover's existing league game against Welling on Tuesday will be rescheduled.
On a cold, grey day, the football was appropriately grim in the opening stages, though Jack Parkinson saw a volley from a Deverdics corner cleared off the line just after the half-hour, shortly after Danny Hall was booked for bringing down Ricky Miller just outside the box.
Will Hatfield broke the deadlock nine minutes before the break when he controlled a looping cross at the back post and stretched to drill a clean half-volley across the face of Rafferty's goal and inside the post.
It should have been 2-0 on 40 minutes when Guiseley won possession in midfield and big Emile Sinclair led a three-on-two break, before rolling left to Gavin Rothery who could only pull his low shot across then face of Rafferty's goal from 12 yards.
Sean Raggett glanced a header straight at keeper Steve Drench from a Nicky Deverdics free-kick as Dover sought a reply before the interval and after the break Ricky Miller looped a tame header over the angle of Drench's goal while an inswinging Deverdics corner bounced along the bar and behind.
The equaliser arrived on the hour when a Deverdics free-kick, awarded after Danny Lowe hauled down Modeste, was tipped over by Drench, and though Raggett's header from the subsequent corner was blocked, Jack Parkinson rammed into the roof of the net from close range.
The game sprung to life and Parkinson tested Drench but it was the Leeds side who sent their small band of fans wild when Gavin Rothery stroked into an empty net on 71 minutes after Rafferty had come out to claim a high cross, only to spill the ball under pressure from Sinclair.
Dover pressed without creating much and the game looked up until Duane Ofori-Acheampong bobbled past Drench with a minute to go after a surging run down the right and low cross from Modeste, who might have won it with a dipping volley jut past the post in injury-time.
Dover: Rafferty, Magri, Raggett, Orlu, Modeste, Bellamy (Ofori-Acheampong 82mins), Miller, Murphy (MUrphy 71mins), Sterling, Deverdics, Parkinson. Subs not used: Walker, Kinnear Jr, Grimes.
Guiseley: Drench, Toulson, Lowe, Lawlor, Rothery, Hall, Hatfield, Dickinson, Sinclair (Boyes 77mins), Atkinson, Hurst (Parker 90mins). Subs not used: Lockwood, Boshell, Dudley.
Attendance: 667.