The south coast club, who last played in the English top flight in 1983, moved up to second in the Championship with four games left, one point ahead of Burnley and one behind leaders Middlesbrough who are both in action on Saturday.
Promotion to the Premier League will ensure a huge windfall this year with a new 5.1 billion pounds ($7.24 billion) domestic TV deal beginning in the 2016-17 season.
Chris Hughton's side took the lead in the 29th minute when Hemed tucked in a penalty after Brighton striker James Wilson was pulled back by Fulham defender Richard Stearman.
Hemed headed in his side's second goal five minutes later and when Spanish defender Bruno made it 3-0 early in the second half Brighton were home and dry.
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Hemed completed his hat-trick with 10 minutes remaining and Anthony Knockaert added a fifth.
Middlesbrough are away at relegated Bolton Wanderers on Saturday while Burnley, bidding to return to the top flight after being relegated last season, travel to Birmingham City.
Fourth-placed Hull City look certain of a playoff place after beating Wolverhampton Wanderers 2-1.
($1 = 0.7040 pounds)
(Reporting by Martyn Herman; Editing by Toby Davis)
