Carpenter met a cross from Nathan Jones with a low drive from 25 yards, his fourth goal of the season.
Both teams were denied by the woodwork in an evenly contested first half. Brighton winger Gary Hart hit the crossbar in the fourteenth minute with a shot from just inside the penalty area.
Brentford midfielder Stephen Evans struck the bar with a free-kick from 25 yards after 32 minutes.
Brentford, deep in relegation trouble refused to fold once they had fallen behind. Striker Tommy Wright, on loan from Leicester, should have equalized with a close range header from a free-kick straight at Brighton keeper Ben Roberts.
Brentford finished the match with ten men. Goalie Stuart Nelson, making his League debut, was sent off four minutes from time for bundling over Brighton sub Jake Robinson.
Midfielder Stuart Talbot had to go in goal as Brentford had already used three substitutes.
Brighton manager Mark McGhee had sympathy for Nelson.
"I thought it was hard on him," McGhee said. "It was clumsy and I can understand the ref sending him off, but Jake still had a bit to do because defenders were covering.""I was very pleased with the performance. It was a difficult night. The ground was practically frozen in places, but we kept our concentration and shape. We were patient and when we got a chance we took it.
"We have now taken seven points from the last three games and that is good form. I think it is going to be like this to the last kick. I think we will need to win in the last game of the season to stay in the play-offs."Brentford boss Wally Downes said: "I couldn't ask for anymore commitment and effort from the players, and I thought on the balance of the game we were unlucky not to get a result."