Barnet came out with attacking intent and Kyei, Coulthirst and Mason-Clark all had efforts come close in the opening quarter of an hour.
Mark Cousins was called into action soon after, making a good save with his feet to deny Cauley Woodrow.
Barnet took the lead on the half-hour mark through a calamitous own goal forced by great pressing by Coulthirst and Mason-Clark.
Atkinson played the ball back towards his ‘keeper Stahl, only for the latter to let the ball roll past him into the net.
At the other end, Cousins pulled off a great save to tip Davies’ dipping half-volley over the crossbar.
In the second half, 2017/18 Player of the Season Dan Sweeney header Dan Sparkes’ corner over the crossbar.
Minutes later, Hilton found himself racing down on Cousins’ goal with half the field to run into. However, Cheye Alexander sprinted back to get around him and cut out the danger.
The hour mark saw John Still begin to make the changes, Barham coming on and linking up with another substitute, Trialist One, who hit a powerful effort at the Fulham ‘keeper.
Adams also came on and dragged a shot from the edge of the box narrowly wide of the left post.
In the dying moments, Wes Fonguck made a smart turn, nutmegging his marker before firing at goal, only to see his shot cannon back off of the crossbar.
Barnet: Cousins (Trialist GK 73), Alexander, Johnson, Reynolds (Adams 59), Robson, Coulthirst, Sparkes (Hinckson-Mars 86), Kyei (Trialist One 59), Boucaud (Fonguck 80), Sweeney, Mason-Clark (Barham 59).
Unused: J. Taylor, Tutonda, Syla, Pascal, Payne, Sule.
Referee: Anthony Swallow