The Midlands League club welcomed North End to Laing Park but the visitors made a flying start, Connor Macleod opening the scoring with just two minutes gone.
But Panumre responded well and Connor Coupe restored parity six minutes later.
The game rushed from end-to-end and had a traditional cup-tie feel to it.
Just before the 30-minute mark North End hit again, Ryan Smith putting the visitors 2-1 up.
The game looked to be put beyond Carnoustie’s reach on 70 minutes when Smith again found the net.
Panmure refused to give up on the cup tie, though, and ensured a nervy finish for the visiting side when Dale Reid made it 3-2 with seven minutes left on the clock.