The Seagulls showed from the start that they were not afraid to come forward and their enterprise was rewarded with the opening goal after seven minutes.
Andrew Davies fouled Colin Kazim-Richards and when Jason Dodd arrowed the free-kick to the far post, Lee Camp was slow to leave his line allowing Dean Hammond time to head home.
A stunned Derby re-grouped and were on level terms after 12 minutes when a long throw by Inigo Idiakez was only cleared to Paul Peschisolido, who chested the ball down before driving it beyond Wayne Henderson from 12 yards.
Despite the setback Brighton continued to enjoy plenty of the ball and went close midway through the half when the impressive Kazim-Richards dragged an angled shot just wide of the far post.
Peschisolido was in lively form and almost plundered his side the lead on the half-hour mark with a 16-yard shot which Henderson managed to smother at the second attempt.
And Derby almost ended the half in front when, in stoppage-time, Idiakez twisted and turned inside the penalty area before unleashing a shot which the keeper fumbled, but his alert defence were able to scramble the loose ball clear.
The home side went even closer shortly after the re-start when Idiakez and Tommy Smith combined to create a clear chance for Michael Johnson, whose header bounced to safety off the top of the bar.
After 50 minutes referee Brian Curson hobbled off to be replaced by fourth official Martin Harris.
Peschisolido was the provider on 58 minutes when, after being forced wide by the keeper, he turned and crossed for Morten Bisgaard to head narrowly over from ten yards.
Despite the pressure, Brighton were still eager to push forward and Leon Knight was close to giving them a freak lead with 20 minutes to go when his deep cross almost caught out Camp, who had to be at full stretch to scoop the ball out from beneath the angle of post and bar.
And Brighton felt deeply aggrieved with seven minutes to go when Johnson was fortunate to escape either a red or yellow card when he hauled back Kazim-Richards, who would have had a clear run on goal.
After the protests had subsided, Knight stepped up to crash the resultant free-kick against a post from 25 yards out.