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.
1. Rob Sanchez 9
Superb reaction save following a deflected effort in the second half then an even better one to deny Ivan Toney's header. Excellent claiming long throws and great distribution. Rarely tested but what he had to do, he did well.
2. Tariq Lamptey 7
Played in a slightly deeper role and performed his defensive duties well. Looked to bomb forward when he could.
3. Adam Webster 7
Returned from a calf injury and eased his way back. Solid display and will improve more with game time.Booked for a second half foul
4. Dan Burn 7
Couple of good early recovery tackles and physical and reliable presence in the heart of the defence in Dunk's absence,