Kieran Ryan gave Emley a 31st-minute lead and the hosts looked on course for the last 32 until Jack Richardson levelled eight minutes from time. Emley’s hearts were then broken when Dickens netted in the final minute to send the visitors through. Both teams played the entire second half with 10 men with Liam Davis sent off for Cleethorpes and Joe Brennan seeing red for Emley.
Pickering Town’s run was also ended but in more comprehensive fashion as visiting Shildon eased to a 5-0 triumph. Hallam were also dumped out after a 4-0 loss at home to Morpeth Town.
Hemsworth Miners Welfare visit Dunston UTS in the Vase second round tomorrow evening.
In the NCE Premier, Thackley moved level on points with leaders Cleethorpes Town through a 3-1 defeat of visiting Barton Town Old Boys. For the hosts, Christopher Wademan’s brace was supported by a Patrick McGuire strike.
But third-placed Liversedge lost ground on the top two after a 2-1 loss at Clipstone, who led 2-0 before Rhys Davies converted a 61st-minute spot kick.
Elsewhere, Garforth Town moved 13th with a 2-1 triumph at Harrogate Railway, who are fifth-bottom.
Luke McCrum bagged a last-minute winner for Garforth for whom Lee Turner equalised on the stroke of half-time after Fraser Hansen had given the hosts a 21st-minute lead.
In Division One, third-placed Knaresborough Town battled to a 2-2 draw at fifth-placed hosts Pontefract Collieries.
The hosts led twice through Jordam Turner and a Christopher Wood penalty but Colin Heath and then Benjamim Cohen both hit back for Boro, with Cohen netting five minutes from time.
Yorkshire Amateur lost a 5-4 epic at home to Brigg Town. An Adam Shaw double plus a goal each from Carl Heard and Daniel Freeman was somehow in vain for the 15th-placed hosts.
Elsewhere, 11th-placed Selby Town lost out 1-0 at Penistone Church.