After a goalless opening 45, Clarke struck a rocket into the top corner after pressuring Bromley defender Chris Bush.
The visitors equalised when Jude Arthurs made goalkeeper Grant Smith pay for a rare mistake.
But it did not matter in the end as Carline finished at the back post following good work by Joel Taylor.
Here are Liam Norcliffe’s player ratings from the game...
But it did not matter in the end as Carline finished at the back post following good work by Joel Taylor.