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Goals by Sean Raggett and top scorer Ricky Miller earned Dover a come-from-behind win over Southport in their FA Trophy Second Round tie at freezing Crabble.
Icy patches removed from the pitch before the game indicated how cold it was and Dover and the game both took some time to warm-up.
Miller's 13th goal of the season decided the contest heading in Ricky Modeste's knock down from Nicky Deverdics' corner.
Miller had a shot blocked early on before Jack Parkinson drilled an effort over the bar.
Southport were making their second trip to Kent in successive weeks after their six-match winning run under new boss Dino Maamria came to an end in a 0-0 draw at Bromley last week.
They took the lead after 26 minutes when Jack Ryan's shot went under the diving Andy Rafferty.
Two minutes later Paul Rutterford got the better of Richard Orlu on the touchline, but his final pass fell short.
Aswad Thomas and Miller went close before Dover pulled level three minutes before half-time.
Deverdics was again the provider - his left-foot free-kick looked to be covered by Port goalkeeper Max Crocombe until Sean Raggett nipped in to flick home his fifth goal of the season.
Orlu headed Deverdics' corner wide of the far post early in the second half and Modeste went off 10 minutes from time with a dead leg to be replaced by Liam Bellamy, his first action since September.
Southport went close when top scorer Louis Almond was put in but Rafferty was off his line quickly to thwart him
Miller was booked late on - having been buffeted all afternoon by a big Southport back four.
Then Southport defender Josh Thompson was also yellow carded for flooring the Dover striker just outside the box,
Dover: Rafferty, Magri, Raggett, Sterling, Orlu, Thomas, Murphy Grimes (Murphy 88mins), Deverdics, Parkinson, Modeste, (Bellamy 80 mins), Miller.
Subs not used: Walker, Diallo, Pinnock
Southport: Crocombe, Challoner, Blakeman, G. Jones (Nolan 67mins), Foster, Thompson, Almond, Wright, Ryan (McCarthy 73mins), Rutherford (Bishop 80mins), Phenix.
Subs not used: A Jones, Viscosi
Attendance: 629