Following an injury in the warm up to Jamie Stephens, Craig Ross was drafted in to make his Barnet debut.
Mauro Vilhete had the first shot of the game 3 minutes in after being given time and space 20 yards out, but his effort curled over the bar.
The first chance for the hosts came on 8 minutes, when 2016/17 Championship Player of the Year Anthony Knockaert brought the ball into the box and Barnet failed to deal with the danger. It fell to Hemed who poked a shot narrowly wide.
Brighton began to dictate the play, controlling the ball well in midfield, but Barnet were more than holding their own when put any under pressure.
In the 19th minute, Vilhete had another shot at goal after neat passing play on the left hand side. His stinging effort from the top corner of the box went narrowly wide.
Just after the half hour mark, David Tutonda was caught in possession and Anthony Knockaert raced through on goal. The Frenchman took too long to get any shot away and when he finally did, Craig Ross was equal to it.
Jack Taylor was the next to have an effort on goal. A Jamal Campbell-Ryce corner fell to Akpa Akpro who set up the 19-year-old who curled a shot narrowly wide, hitting the stanchion behind the goal.
A minute later, the Bees had penalty appeals waved away by referee Stephen Martin. Shaq Coulthirst latched on to a loose back pass and seemed to be taken out by goalkeeper Niki Maenpaa.
Brighton broke the deadlock shortly after the restart. Liam Rosenior’s shot was by Clough only to fall into the path of half time substitute James Tilley who slotted home.
The goal really seemed to bring Barnet to life however. A corner shortly afterwards was played short and whipped in by Jack Taylor. Coulthirst flicked it on to Campbell-Ryce who saw his effort well saved, it then fell to Santos who could only put it into the side netting.
On the hour, Hemed had a weak effort at goal easily saved by Ross.
68 minutes in a Barnet struck the post. Harry Taylor sent Jean-Louis Akpa Akpro through on goal but his shot was deflected by the covering defender onto the upright.
Skalak had an effort from distance comfortably saved by Ross with 15 minutes left to play.
Chances for Jack Taylor, David Tutonda and Ruben Bover all came and went in the final few minutes and, despite all the pressure, it just wasn’t to be for Barnet.
The Bees were backed by an impressive 678 travelling supporters who sang their hearts out throughout the 90 minutes.
BARNET: Ross, Clough, Santos, Campbell-Ryce (Akinola 63′), Coulthirst (Amaluzor 69′), J. Taylor, Tutonda, H. Taylor, Fonguck, Vilhete, Akpa Akpro (Bover 75′).
Unused subs: Kyei, Shomotun, Smith.