The Blues were struck by ill-discipline yet again just before half-time at Stamford Bridge, seeing a captain sent off for the second time in as many games following Reece James' red card in the 4-1 thrashing by Newcastle last weekend that Mauricio Pochettino called the worst display of his tenure so far.
Gallagher, already on a yellow card following an earlier foul on former Chelsea starlet Billy Gilmour, received a second in first-half stoppage time for a mistimed sliding challenge on Facundo Buonanotte.
Such a dismissal came just two minutes after Argentine attacker Buonanotte had cut inside Levi Colwill off the right flank and curled past former team-mate Robert Sanchez to halve Chelsea's two-goal lead, given to them after early close-range headers from set-pieces from Enzo Fernandez and Levi Colwill.
It was Fernandez's first Premier League goal since his then British record £106.8million switch from Benfica in January, while it was Colwill's first of any description in Chelsea colours against the club for whom he starred on loan last term.
However, injury-hit Brighton could not make the most of their man advantage after the interval, with Chelsea restoring their two-goal cushion through Fernandez's cool penalty after James Milner's challenge on Mykhailo Mudryk led to referee Craig Pawson pointing to the spot after being advised by the VAR to consult the pitchside monitor.
Substitute Joao Pedro's flicked header at the start of 10 minutes of second-half stoppage time set up a hectic grandstand finish, but Chelsea just held on despite more officiating confusion after a Simon Adingra cross was blocked by Colwill and Brighton were awarded a 100th-minute penalty for handball.
However, Pawson's decision was rightly overturned after he was told to consult the monitor, with the ball clearly striking Colwill on the head as Chelsea held out for a valuable three points in their quest for Europe ahead of a trip to Manchester United in midweek.