ON TARGET: Ryan Turner.
Ryan Turner's 60th-minute strike put the visitors in control of the key game in the bottom half of the Toolstation Premier.
A neat move saw Turner grab his fifth goal of the season after moving onto a slide-rule pass from Ian Patchett.
Stan Paxton then had the chance to double the lead in a one-on-one.
But his effort was tipped onto the post by the goalkeeper and grabbed at the second attempt as the ball trickled along the line.
With Barum not making their final pass count, Melksham found space to equalise with a far-post header in the last 10 minutes.
The draw means Melksham remain in the relegation zone while Barnstaple are just three places and two points above them.
See Thursday's Journal for a full report and reaction from the game.
Barnstaple Town: Jamie Pow, Ian Patchett, Paul Quinn, Jamie Frickleton, Matt Hare, Shane Tolley, Andrew Rogers, Matt Deakin, Richard Elston, Stan Paxton, Ryan Turner. Subs: Luke Austen, Tom Moody, Joe Price.