Two first-half goals from leading goalscorer Matty Fryatt put the Foxes in control before the Seagulls launched a thrilling second-half fightback.
Steve Howard had an effort ruled out for offside before Fryatt put the Foxes ahead with a low shot after goalkeeper John Sullivan blocked a centre by Max-Alain Gradel.
Fryatt doubled the advantage at the far post only three minutes before the break, cashing in from two yards out when a shot by Gradel spun across the goalline.
Brighton midfielder Bradley Johnson, on loan from Leeds, reduced the deficit with a low 25-yard drive on the hour and then levelled with another long-range effort after 85 minutes.
Albion grabbed their first home league win of the season with a minute left when Hobbs, on loan from Liverpool, turned a Joe Anyinsah cross into his own net under pressure from substitute Dean Cox to inadvertently hand Leicester their first away league defeat of the season.