The former Valencia star, making only his fourth start since joining Gus Poyet's side in August, set up goals for Inigo Calderon and Ashley Barnes as the Seagulls bounced back from their first defeat of 2012 at Blackpool on Saturday.
Kazenga LuaLua's livewire wing play also gave Derby sustained problems, although Nigel Clough's men threatened to draw level before Barnes sealed the points midway through the second half.
Vicente departed to a standing ovation eight minutes from time, shortly after the crossbar denied him the the goal he deserved.
Poyet's side move to fourth in the table, a position they will retain unless Blackpool beat Leicester on Wednesday, while Derby remain 12th.
Calderon and Lewis Dunk made their first starts since February in the Brighton defence in place of Adam El-Abd and the suspended Gonzalo Jara Reyes, while Kazenga LuaLua and Sam Vokes came in for Craig Noone and Craig Mackail-Smith.
James Bailey made his first Derby start in midfield, while Nathan Tyson and Steven Davies were restored in attack as Nigel Clough's men chased a third consecutive win.
Vicente's set piece delivery gave Brighton the lead at the weekend before the 3-1 defeat at Bloomfield Road and the Spanish midfielder was the provider once more as the hosts claimed an early advantage.
Barnes had a ninth minute header deflected behind and from the resulting corner Calderon stooped to head home Vicente's centre.
Bailey fired a speculative effort wide as Derby sought an immediate response, while Tyson drilled a 19th minute volley at Seagulls goalkeeper Peter Brezovan.
Brighton continued to enjoy the lion's share of possession, with LuaLua demanding the full attention of Derby full-back Tom Naylor.
When the former Newcastle attacker found space in behind the Rams defence before the half-hour his touch deserted him.
Derby eased their way into the contest as half-time approached with Theo Robinson, Tyson and Davies combining to good effect, the latter dragging a 35th minute shot narrowly wide from inside the area.
Vicente tested visiting goalkeeper Frank Fielding early in the second period before Derby enjoyed a sustained spell of pressure.
Centre-back Jake Buxton was proving a nuisance at set pieces, directing a pair of headers over the bar, while Paul Green timed his run from midfield superbly to nod Robinson's cross inches wide in the 55th minute.
Lua Lua collected a pass from Vicente to draw an excellent fingertip save from Fielding with an hour gone and Brighton's two outstanding players on the night combined to craft the game's decisive goal.
Vicente marauded forward from midfield to tee up LuaLua, who attacked the Derby backline once more before providing a return pass for the playmaker to give Barnes a simple finish.
The goal Vicente's performance merited failed to arrive as Fielding pulled off a smart save from 25-yard drive and a jinking run resulting in the crossbar being rattled.
Derby gallantly produced a late rally as Brezovan thwarted Jeff Hendrick one-on-one and substitute Callum Ball became the latest player to pass up a headed opportunity.