Will Buckley put his side ahead in the ninth minute before Matt Upson scored his first goal in a Brighton shirt from six yards out 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.
The Seagulls were quickest out of the blocks with Buckley causing Blackpool's defenders all sorts of problems in the early stages. The former Rochdale man tried his luck from range in the opening minute but his effort was gobbled up by Tangerines stopper Matt Gilks.
Gus Poyet's men continued to dominate and it came as no surprise when they broke the deadlock in the ninth minute.
Brighton poured forward in numbers and Barnes played the ball forward to Buckley, who cut inside before curling the ball high into the corner of the net from 20 yards out, leaving Gilks stranded.
Further misery was piled onto Blackpool in the 23rd minute when Orlandi's fantastic cross was headed back across goal by Inigo Calderon and Upson bundled the ball home from close range to make it 2-0.
Albion made it 3-0 on the brink of half-time when Orlandi played a wonderful one-two with Lopez before finding the bottom corner of Gilks' net with a neat finish with the outside of his foot.
Brighton began the second half as they ended the first and Lopez made it four within two minutes of the re-start. Barnes flicked the ball on to Lopez on the edge of the box and his deflected effort went into the roof of the net.
Tom Ince had a couple of opportunities to get on the scoresheet in the early stages of the second half but it was Matt Phillips who set up his side's goal.
The former Wycombe winger launched the ball into the area in the 53rd minute and his cross was turned into his own net by Hammond.
Brighton made two further substitutions with Kazenga LuaLua and Bruno Saltor replacing Buckley and Wayne Bridge respectively. LuaLua made an instant impact four minutes after coming on when he crossed for Barnes to tap in from close range to make it 5-1.
Barnes made it six in the 90th minute when he stroked the ball home from Orlandi's cross.