Defender Duffy struck with a bullet header from a corner after 10 minutes to give the hosts the perfect start.
Watford then gifted Brighton their second a few minutes before the interval when they lost the ball trying to play out from the back and Maupay curled home.
The visitors did improve after the break and had a goal by Emmanuel Dennis ruled out for offside, but Brighton were comfortably the better side as they moved to six points.
It is the first time Brighton have started a top-flight season with back-to-back wins, and the only blemish was an injury to Maupay who did not come back out for the second half after appearing to hurt his shoulder.
Graham Potter's well-drilled Brighton side were in command once Duffy, who suffered a difficult last season on loan at Celtic, rose highest to power in a Pascal Gross corner.
It was a case of back to reality for Watford who marked their return to the top flight last week with a 3-2 win over Aston Villa at Vicarage Road.
But for Brighton manager Graham Potter these are heady days with his side looking capable of residing in the top half.
"Back to back wins at any stage are hard to achieve. We are in a good place, but it is just a start," he said.
On Maupay's injury Potter said: "It's early, but we are hopeful. Days more than weeks. But it is disappointing for him as he was doing really well."
Watford manager Xisco Munox took heart from a better second half display but said his side must learn from their mistakes.
"Everybody knows the Premier League is the best league in the world," he said. "It's important everybody stays together.
"I promise you we're working very, very hard. It's one step back, but we have to try to make two steps forward."