After seeing an early penalty claim denied, Conlan received the ball and fired home a beauty halfway through a first half that saw the hosts dominate.
Wellington came into the game after the break and during an improved showing, equalised through sub Oli Nott near the hour mark.
But the impressive Conlan wasn’t to be denied and with a minute of normal time remaining, the striker scored the winner with a fantastic strike that left Wellington keeper Jake Viney powerless.