Israeli international Hemed scored twice in the first half, before he completed his hat-trick 11 minutes from time after Bruno had netted his first goal of the season early in the second period.
Anthony Knockaert delightfully curled home a late fifth as Albion moved above Burnley into second with a third successive win, which also extended their unbeaten run to ten games.
Fulham enjoyed plenty of possession in the early exchanges as Albion struggled to get going against a Cottagers side who went into the match on the back of three successive wins.
Fulham’s 21-goal striker Ross McCormack had a low 20-yard shot saved by Albion keeper David Stockdale on nine minutes, before Fulham stopper Marcus Bettinelli back-peddled to push over Beram Kayal’s cross shot after 17 minutes.
The game changed in the 29th minute with referee Andy Woolmer’s decision to award Albion a penalty - the 11th conceded by Fulham this season. James Wilson was pulled back by Fulham defender Richard Stearman, with the visitors furious at the decision but Hemed - who scored the winner from the penalty spot at Craven Cottage in August - sent Bettinelli the wrong way from 12 yards.
That shell-shocked Fulham who fell 2-0 behind just five minutes later when Hemed brilliantly headed home Anthony Knockaert’s inswinging free kick.
Things almost got worse for the visitors before half-time but Bettinelli kept out Wilson’s dink after a driving run by Kayal.
At the other end, McCormack blazed a free kick wildy over as Albion took a two-goal lead into the break.
Brighton extended their lead nine minutes into the second half when Jiri Skalak’s corner reached Bruno at the back post and he took a touch before firing home his first goal of the season.
McCormack had a great opening from Moussa Dembele’s low centre five minutes later but side-footed over, before Knockaert shot straight at Bettinelli from 25 yards just past the hour.
Stockdale was called into action to produce a superb double save to deny Fulham sub Lasse Vigen Christensen on 66 minutes, before Bettinelli denied Hemed his hat-trick after a superb run by Wilson two minutes later.
Albion keeper Stockdale superbly tipped over Emerson Hyndman’s powerful effort as the game entered the final 20 minutes.
Hemed did complete his first Albion hat-trick on 79 minutes when Dale Stephens’ low shot took a deflection and he turned the ball home from ten yards, with Fulham appealing for offside.
It was then a case of how many Brighton would score and after Knockaert had an effort pushed over and substitute Steve Sidwell was denied by a goal-line clearance, Knockaert placed the ball into the far corner from 18 yards for the Seagulls’ fifth on 86 minutes.
BRIGHTON: Stockdale; Bruno, Goldson, Dunk, Rosenior; Knockaert, Stephens, Kayal, Skalak (LuaLua 81); Wilson (Murphy 82), Hemed (Sidwell 81). Subs: Maenpaa, Greer, Baldock, Bong.
FULHAM: Bettinelli, Stearman, Fredericks, Parker (Christensen 58), Ream, Tunnicliffe, O’Hara (Baird 64), Dembele, Hyndman, McCormack, Amorebieta (Woodrow 75). Subs: Lonergan, Richards, Garbutt, Smith.
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