Inigo Calderon made an impressive return from injury with a hand in both of Albion's goals, which were scored by Ashley Barnes in the second minute and Andrea Orlandi after 25.
The Spaniard might have got on the scoresheet himself at the start of the second half but his glancing header went wide.
Jeff Hendrick did pull a goal back midway through the second half but the Rams never really looked like rescuing anything from the game.
Less than 80 seconds were on the clock when Brighton took the lead with a beautifully crafted goal. Calderon spotted David Lopez breaking into the right-hand side of the penalty area and Lopez picked out a low pass which set up Barnes to tap in from very close range.
Soon afterwards, the hosts extended their lead with a goal made in Spain. Lopez teed up Calderon who whipped in a cross from the right and Orlandi got in front of his marker to thump a header into the roof of the net, leaving Rams goalkeeper Adam Legzdins with no chance.
The roles were almost reversed three minutes after the break when Orlandi's cross was headed wide by Calderon, who failed to make proper contact with the ball.
Brighton almost went 3-0 ahead after 63 minutes, hitting the visitors on the counter-attack. Lopez, on the right, released Will Buckley with a perfectly-timed diagonal pass but his shot was blocked by Legzdins.
The Albion striker was denied by Legzdins again soon afterwards, this time from point-blank range, before the rebound was scrambled off the line by a defender.
What had looked like a stroll in the rain suddenly turned into a nervous finale for Gus Poyet's side when Hendrick got a touch to Jamie Ward's driven free-kick to divert the ball past Tomasz Kuszczak.