Cole Palmer put them in front when he headed his 22nd league goal of the season in the 34th minute.
Christopher Nkunku’s 64th minute strike put Chelsea further ahead before Blues defender Reece James was sent off for kicking Brighton’s Joao Pedro.
Danny Welbeck reduced the deficit in stoppage-time, but Chelsea held on to secure a fourth consecutive league victory for the first time since October 2022.
With Newcastle losing 3-2 at Manchester United in Wednesday’s other game, Chelsea moved above the Magpies.
The Blues will be guaranteed a place in next season’s Europa League if they avoid defeat against Bournemouth at Stamford Bridge on Sunday, or if seventh-placed Newcastle fail to win at Brentford.
Chelsea could even finish fifth if they beat Bournemouth and Tottenham lose at Sheffield United.
It is an impressive recovery masterminded by Pochettino, who has faced criticism throughout his troubled first season in charge.