In-form Hemed made it five goals in four games as he helped himself to a brace as Albion hauled themselves back to the top Championship - for a few hours at least.
Baldock on his return from injury was also on the scoresheet as he notched his 100th career goal as Albion dominated the second half against Nigel Clough's side.
Michael Kightly did pull a goal back for the visitors as he expertly curled home a free kick, but Glenn Murray came off the bench to get in on the Albion act in the closing stages and complete the victory.
Their first league win in three put them back to top of the table with Newcastle not playing until the weekend's late kick-off.
Brighton rung the changes to the side that netted a late-equaliser at Brentford last Sunday as Dale Stephens and Badlock returned from injury as Lewis Dunk was back after his one-game ban. Solly March and Hemed were also back in the starting XI as Chris Hughton made five changes.
Murray, Jamie Murphy and Oliver Norwood all found themselves on the bench, while Uwe Huenemeier and Jiri Skalak were not included in the squad.
The first chance went the home side's way on six minutes as a Hemed cross was headed away by Tom Naylor at the far post, it fell nicely to Steve Sidwell on the edge of the box, but his volley flew wide.
Just six minutes later, Albion led. A great switch by March put Knockaret away on the left, the winger drove at Tom Flanagan and put a teasing low cross through a sea of bodies in the six-yard box, with Hemed pouncing to find the far corner.
Moments later, Knockaert again skipped forwards, this time through the middle, but his effort from 24 yards was comfortable for Jon McLaughlin in the Brewers' goal.
Flanagan was alert on the 25-minute mark as he put in some strong shepherding to block out Baldock after Bruno had poked a clever ball through on the right of the area.
Despite the cold, Knockaert looked fired up, maybe spurred on after taking an early boot from a Burton counterpart. But it was Burton right-back Flanagan that looked the pained one as Knockaert continued to cause problems out wide.
Burton had a couple of half-hearted ventures forwards, but caused few problems with David Stockdale a bystander for much of the half, although the away players felt they should have had a penalty when Lucas Atkins went down in the box under pressure from Stephens.
The home side could and probably should have made their first-half dominance count as the clock ticked into added time, but March's cross from the byline whistled across the goalmouth without a touch.
Albion made it 2-0 within two minutes of the second half as March broke down the right, drove into the box and Baldock guided his low cross into the net from close range. Back at the other end, Brighton continued to shut out their visitors as Dunk put in a crucial block to stop a key cross into the box.
But Albion were finding their stride as a neat and patient passing move saw March collect the ball on the edge of the box and skip past a tackle, before being forced to the ground by John Mousinho. Referee Stephen Martin pointed straight to the spot and Hemed sent McLaughlin the wrong way for his second of the afternoon.
With 20 minutes left to go, Marvin Sordell dispossessed Dunk in the box and bore down on goal, but Stockdale did superbly to beat away his effort from close range.
Chris Hughton handed Chuba Akpom his home debut as he, Murray and Beram Kayal all came off the bench in a rare triple change.
With 15 minutes left to play, the visitors did pull a goal back as, after Dunk gave away a free kick just outside the box, Kightly expertly curled home into the top corner via the inside of the upright.
But Murray notched his first goal since December and his 16th of the season with seven minutes remaining as he headed home Knockart's cross.
Arsenal loanee Akpom could have made it a home debut to remember with two minutes left as he cut back in the box, but curled wide of the far post.
Brighton: Stockdale; Bruno, Duffy, Dunk, Pocognoli; Knockaert, Stephens (Kayal 73), Sidwell, March; Baldock (Akpom 73), Hemed (Murray 73). Subs: Walton, Tomori, Norwood, Murphy.
Burton: McLaughlin, Flanagan, Mousinho, Turner, Sordell (Miller 84), Akins, Naylor, Vigen Christensen (Varney 80), Knightly, Murphy (Palmer 58). Subs: Bywater, Williams, Harness, Barker.
Attendance: 29, 454.