Will Buckley put his side ahead in the ninth minute before Matt Upson scored his first goal in a Brighton shirt from six yards 14 minutes later.
Andrea Orlandi made it 3-0 in the 45th minute before David Lopez scored straight after the half-time break. Dean Hammond's own goal made it 4-1 before Barnes added two late goals on his return.
The hosts were boosted by the return of striker Barnes who came back from a seven-match ban he picked up for appearing to trip referee Nigel Miller in his side's 1-0 defeat to Bolton in March.
Gus Poyet's men dominated the early exchanges and went ahead after nine minutes when Buckley cut inside before curling the ball high into the corner of the net from 20 yards. The Seagulls doubled the advantage in the 23rd minute thanks to Upson, who bundled home Inigo Calderon's header.
Albion made it 3-0 on the stroke of half-time. Orlandi and Lopez neatly combined before the former found the bottom corner with the outside of his foot.
Brighton were rampant and made it four shortly after the restart when Lopez's deflected effort beat Matt Gilks.
Blackpool were shellshocked but grabbed a consolation through Hammond, who turned a Matt Phillips cross into his own net.
It made no difference, though, and Brighton struck twice late on through Barnes. First, he tapped in Kazenga LuaLua's cross from close range, and then in the 90th minute stroked home from Orlandi's cross.