In a repeat of last season's fourth qualifying round game, Dickson volleyed home from James Hammond’s cross to fire the Hornets into the third qualifying round.
And the winner was a just reward for Horsham, who dominated their National League South opponents in the second half.
Shamir Fenelon struck the post for the Hornets in a first half short of clear-cut chances – but Horsham were superb in the second half.
Wanderers keeper Harry Foulkes produced an excellent double-save to deny both Dan Ajakaiye and Isaac Philpot early in the half.
Ajakaiye then saw an effort scrambled off the line by George Francomb, and Hammond cracked the crossbar as the Hornets ramped up the pressure.
Foulkes came to Dorking’s rescue twice in a matter of minutes, brilliantly keeping out Joe Turner before doing so well to stop Dickson one-on-one.
But Horsham weren’t to be denied, as Dickson fired home with six minutes to go to spark delirious scenes at the Fusion Aviation Community Stadium.
The draw for the FA Cup third qualifying round will be published at 1pm on Monday (September 16).
No new clubs will enter the draw at this stage.
See some of John Lines’ pictures from the game on this page and the ones linked, and read Horsham manager Dominic Di Paola’s thoughts in the West Sussex County Times, out every Thursday.
1. FA Cup: Late strike propels excellent Horsham FC past Dorking for the second year running - in pictures
Action from Horsham v Dorking Photo: John Lines
2. FA Cup: Late strike propels excellent Horsham FC past Dorking for the second year running - in pictures
Action from Horsham v Dorking Photo: John Lines
3. FA Cup: Late strike propels excellent Horsham FC past Dorking for the second year running - in pictures
Action from Horsham v Dorking Photo: John Lines
4. FA Cup: Late strike propels excellent Horsham FC past Dorking for the second year running - in pictures
Action from Horsham v Dorking Photo: John Lines