Substitute Ryan Peters appeared to be brought down just outside the box as he prepared to pull the trigger on 68 minutes but Melin surprised even Brentford fans by pointing to the spot and sending off offender Stevland Angus.
Kevin O'Connor's penalty was saved but John Mousinho cut short the Barnet celebrations by ramming home the rebound.
An earlier O'Connor penalty had given Brentford the lead just after half-time when Max Porter brought down Charlie Ide.
Terry Butcher's men though had been reduced to ten just before the break when debutante Lee Thorpe walked for a two-footed lunge on Porter.
It was a nightmare for Thorpe who had sat out Brentford's first three games courtesy of a red-card for Torquay at the end of last season.
The hulking striker headed over with the only real chance of a lacklustre first half, which only really ignited with his sending off.
Barnet nearly made the extra man count after the break before Angus's red card when Danny Hart, Jason Puncheon and Anthony Thomas all went close .
And it was Thomas who could have clinched a point for Paul Fairclough's men at the death but he fired over an empty net in injury time after home keeper Ben Hamer had spilt the ball.
Puncheon had earlier leveled for Barnet on 61 minutes cutting inside to fire home from 20 yards but he could well have got his marching orders as well when he scythed down Mousinho but the challenged went unpunished.
However his strike will have had watching Premiership scouts drooling as the transfer window prepars to slam shut and Barnet boss Fairclough admitted his star man has the quality necessary to play at the highest level.