Anya fired the Hornets into an early lead with an angled shot across Tomasz Kuszczak and Beppe Sannino's side were assured of their first win of 2014 on the hour mark when Forestieri made the most of a poor backpass from Gordon Greer.
Watford had gone into the game on the back of a dismal run of league form which had seen them win only one of their previous 15 matches, but they took the lead with their first attempt of note in the 13th minute.
Alexander Merkel fed Anya on the left-hand side of the penalty area and, after teasing the Seagulls defence, the Scotland international hit a low shot across Kuszczak and into the far corner of the net.
The Seagulls continued to offer very little going forward and they were fortunate not to concede a second goal in the 26th minute.
Marco Cassetti dispossessed Stephen Ward and advanced before clipping a fine delivery into the penalty area where Forestieri found space but tamely side-footed a volley into Kuszczak's arms from six yards out.
Brighton were forced into a change five minutes before the break when the injured Jake Forster-Caskey was replaced by Kazenga LuaLua and it was the substitute who nearly equalised shortly before half-time.
LuaLua received the ball on the left side of the penalty area and surprised everyone by hitting a left-footed shot which flew past helpless Hornets goalkeeper Manuel Almunia and rebounded off the underside of the crossbar.
Brighton started the second half positively as they sought to get back on terms but they continued to be largely restricted to shots from range as David Lopez, Keith Andrews and Dale Stephens chanced their arm.
But Watford were soon back on the front foot, with Troy Deeney slicing a half-volley wide from just inside the penalty area, before the home side doubled their advantage in the 60th minute.
Good pressing by Merkel forced Greer to attempt a back pass which fell well short of its intended destination as Forestieri latched on to the loose ball and rounded the stranded Kuszczak before keeping his composure to roll the ball into the unguarded net.
The Seagulls thought they had pulled a goal back midway through the second half when Leonardo Ulloa headed a free-kick from the right past Almunia, but it was disallowed for offside.
That was to be Brighton's last opportunity of note as the Hornets finished the game with three debutants on the pitch, with Samba Diakite and Park Chu-young introduced as late substitutes to join Daniel Tozser.