Stockport held their own early on and Adam Griffin's long-range drive was saved by Willy Gueret before Puncheon's 25th-minute wonder-strike put the Dons ahead. The skilful winger collected Stephen Gleeson's pass and belted a swerving left-foot drive past Owain Fon Williams and into the top corner from 30 yards.
The goal sparked the Dons into life and Easter doubled their lead three minutes later with a close-range header from Danny Woodards' cross.
On-loan West Ham midfielder Quashie made it 3-0 when he curled the ball home from 12 yards three minutes after the break before Thompson pulled a goal back, drilling low past Gueret from seven yards after Puncheon had sliced his clearance.
But Puncheon made amends with seven minutes remaining as he superbly chipped Fon Williams from 20 yards to round off the win in style.