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.
5. Marc Cucurella 8
Similar to Lamptey as he performed a more defensive role.Very good in possession and linked well with Moder. Brillinat clearance off the line in the second half
6. Alexis Mac Allister 7
Looked lively early and looked to make the most of his return to the starting XI. Would have impressed Graham Potter and in contention for Chelsea
7. Adam Lallana 7
Captain in Dunk's absence. Led the press as soon as Brighton lost the ball. Experience vital in the middle of the park
8. Enock Mwepu 7
Blazed one early chance wide but nice assist for Trossard's goal with a ball over the top. So much energy and one of his best displays in an Albion shirt. Well played.