Albion went 1-0 ahead in the 34th minute courtesy of a volley from Leandro Trossard.
Enock Mwepu delivered a long ball over the top from the halfway line and Trossard sent a brilliant first-time finish over advancing Bees goalkeeper Alvaro Fernandez.
Brighton doubled their advantage to 2-0 three minutes before the break as Maupay scored against his old club.
The French forward collected the ball from Jakub Moder before unleashing a stunning effort into the top right corner from the edge of the box.
Brighton were also thankful to Rob Sanchez for two excellent saves in the second half.
Scroll down and click through to see who shone and who struggled for Brighton against Brentford.
9. Jakub Moder 7
Nice work in the build up to the Maupay goal and another solid display in the Albion midfield. His runs behind the Brentford defence continually stretched them
10. Leo Trossard 9
Gets a nine for that moment of magic alone. What a finish and shame there were not more in the crowd to witness it live. Fourth of the season for Trossard and his second against Brentford. Subbed at halftime for Welbeck
11. Neal Maupay 9
Three in his last three starts and seven goals in total for Maupay so far this season. Great hit and worked hard throughout.
12. Danny Welbeck 6
On in the second half for Trossard and his first appearance since injuring his hamstring in September.