Blackpool could have taken the lead in just the second minute but from a vicious in-swinging corner, captain Michael Jackson couldn't keep his effort down from a matter of yards out.
The home side responded well, first from Skularson whose deflected, dipping shot saw visiting keeper Rhys Evans push away, before a dangerous cross from full-back Kevin O'Connor was headed behind for a corner.
However, as the half wore on, the visitors began to look the most likely to score and they came within inches of doing just that when Keith Southern's superb diving header from Keigan Parker's free-kick crashed back off the inside of the post.
Paul Tierney then tried his luck from long-range as 'Pool looked to capitalise on their possession and only a sliding block from Andy Frampton prevented Adrian Forbes' low-driven cross being tapped home.
They continued to press as the half came to an end and should have gone into the break ahead when a three-man move involving David Fox and Parker resulted in Scott Vernon being put clean through but keeper Clark Masters ensured Brentford stayed on level terms with a fine block.
The second half continued where the first had left off with a superb weaving run by Forbes only matched by a magnificent one-handed save from Masters, low to his right.
However, the Bees should have gone in front moments later when an improvised over-head kick from Skulason in the box fell at the feet of substitute Gavin Tomlin but he somehow miscued and missed a tap-in.
That opportunity seemed to spur the home side on and with 15 minutes left on the clock, they went in front when Rhys Evans failed to deal with a speculative cross. The ball looped up in the air and as it seemed to take an eternity to drop down, Skulason was on hand to bundle it over the line.
With the crowd now fully vocal, the home side's performance went up a level and even though they had to withstand six minutes of injury time, they held on for the win.