The 24-year-old struck twice before half-time, his second a sublime, curled finish into the top corner after he had slotted in from Jamie Vardy’s blocked shot.
Vardy, making a record-equalling 222nd Premier League appearance for the Foxes, scored his side’s second from James Justin’s low cross.
A breathless opening period had included great chances for both sides, as Mat Ryan denied Marc Albrighton inside the first five minutes and Kasper Schmeichel was equal to attempts by Alireza Jahanbakhsh and Danny Welbeck as Brighton threatened on the break.
With the points secured before the interval, Brendan Rodgers’ side comfortably saw out a much quieter second period to move one point behind Tottenham and Liverpool, after both were held to draws on Sunday.
Brighton remains 16th but are now just two points above the relegation places following Fulham’s draw against the champions.
Maddison hints at a return to best in an impressive win
Aware many of their expected top-four rivals had dropped points over the course of the weekend, Leicester’s motivation to take full advantage at the King Power Stadium was evident in their high-octane start.
Maddison’s first-ever Premier League double and Vardy’s 10th goal of the campaign were deserved reward for a superb, free-flowing first-half display, in which the Foxes landed 13 shots at goal.
Vardy’s first opportunity came when his first-time hit from Justin’s excellent pass was saved by Ryan – and he also struck the post before making no mistake when Justin again delivered from the right.
Equalling Muzzy Izzet’s appearances tally, Vardy then teed up Maddison – whose sole England cap arrived over a year ago – for his excellent left-footed finish, which typified a performance indicative of a player nearing a return to his best.
Despite missing a number of key players to injury, defenders Caglar Soyuncu and Timothy Castagne among those still absent, Rodgers’ side continue to apply pressure at the summit in a start which has also seen them successfully juggle their Europa League commitments.
Converting their good start – reignited by this showing and Vardy’s late Bramall Lane winner last weekend that ended a four-game winless run – is a must for Leicester, after last season’s collapse which began over the Christmas period.
On this evidence, they are in good shape to do so ahead of key meetings with Everton, Tottenham, and Manchester United in the next 13 days.