The extra preliminary round tie looked like it was heading for a replay until Dean cut inside to fire home the only goal of the game with 10 minutes to go.
Ar Tarn’s winning start to the new season means they will now host London Colney for a place in the first qualifying round on August 20.
Wellingborough Town were unable to make it through, however, as they were beaten 3-1 by Stotfold at the Dog & Duck.
Rothwell Corinthians play their extra preliminary round clash at Crawley Green this afternoon (Sunday, 3pm).
Whitworth held off a late fightback from local rivals Thrapston Town to kick-off the new ChromaSport & Trophies United Counties League Division One season with a 4-3 success.
The Flourmen were 2-0 up at the break through Cavell Jarvis and Remy Brittain and the game looked done and dusted when James Gorman and Matty Judge struck to make it 4-0 just past the hour.
Liam Carter pulled one back for Thrapston and they had a glimmer of hope when Wayne Brown headed home to make it 4-2.
Carlos Lewis converted a stoppage-time penalty to bring them within a goal of the hosts but that was the end of the scoring.
Irchester United also got off to a winning start as Ty Clark’s goal proved to be enough to give Steve Sargent’s side a 1-0 success at Woodford United.
Raunds Town went down 2-1 at home to Oakham United and Burton Park Wanderers also tasted defeat on their own ground as Buckingham Town ran out 4-1 winners at Latimer Park.
Stewarts & Lloyds, meanwhile, suffered a 3-0 defeat at Lutterworth Athletic.