After being denied a penalty late in the first half, March gave his side the lead in the 47th minute as Brighton won the ball high up the pitch and Kaoru Mitoma slid it into March’s path for a simple finish.
The 28-year-old added a brilliant second six minutes later, latching on to Evan Ferguson’s pass and digging the ball out from under his feet to fire it home inside the far post.
Making his first start since joining Liverpool from PSV Eindhoven in December, Dutch forward Cody Gakpo was anonymous for much of the game as the visitors struggled to keep possession and create any decent chances.
Marsh rounded off an excellent performance by teeing up substitute Danny Welbeck with a glancing header from a throw-in, and Welbeck lifted the ball over a defender before slotting it into the net for his first Premier League goal of the season.
The win means Brighton rise to seventh in the table on 30 points, two ahead of Liverpool, who have struggled with form and injuries.
Additional reporting from Reuters