Niall Davie gave Carlton the lead from the penalty spot on 16 minutes after Danny South brought down Liam Moran
Home goalkeeper Ben Bottomley saved well from Ollie Clark and Lewis Durow before Lewis Dennison scored directly from a corner 15 minutes into the second half.
Both sides went for a winner with Carlton's Nat Watson going closest, crashing a superb shot against the crossbar in added time.
Carlton remain eighth in the table with 64 points from 37 games. They return to action on Saturday when Brighouse Town visit Stoke Lane.
A full report on today's game will be on site tomorrow.