Barnes was the hero by setting up Albion's equaliser and then netting a dramatic winner to down the plucky Grecians at St James Park.
Exeter struck first in the first half. Just eight minutes were on the clock when a cleared corner was played back into the box by Liam Sercombe and Matt Taylor headed the ball into the path of Richard Logan, who swivelled to lash the ball into the net.
Both teams were playing some sparkling football, but it was not until the second half that Brighton really upped the ante.
The equaliser duly arrived in the 64th minute when Barnes crossed from the left and Glenn Murray rose highest to head the ball in off the upright.
Exeter came back strongly after the goal though and could have won themselves in a thrilling finale when Ryan Harley's 25-yard rocket rebounded back off the crossbar, but Barnes won it for the Seagulls in the last minute when he slotted home at the far post from Elliott Bennett's cross.