The U's started brightly and went ahead after 16 minutes. After Seagulls goalkeeper Casper Ankergren had parried John-Joe O'Toole's shot, Tommy Elphick fired straight at team-mate Inigo Calderon, whose fluffed clearance allowed Ian Henderson to convert from close range.
Ankergren had been caught by Henderson's challenge two minutes before the goal and was replaced by Peter Brezovan soon after.
Henderson and Ashley Vincent went close for the hosts and Brighton's best chance of the first half came six minutes before the break when goalkeeper Ben Williams denied Barnes' header.
And after Brezovan denied both Henderson and David Mooney in quick succession, Brighton equalised with 18 minutes to go through Barnes, who converted Elliott Bennett's cross at the near post.
Williams pushed Elphick's effort over and Chris Wood headed wide in stoppage-time for Albion but the champions were held.