The Rams produced a slick performance at Bloomfield Road - despite going behind to David Goodwillie's first-minute effort - with Scotland international Bryson at the heart of everything.
Chris Martin levelled matters before Bryson laid on a second for Patrick Bamford and then bagged the third himself, all inside the first half an hour to increase the Tangerines' relegation concerns.
Blackpool interim boss Barry Ferguson said in his programme notes he wanted to "put things right" following their 2-1 home defeat to lowly Yeovil.
And the Scot got the response he wanted after just 20 seconds when the Tangerines grabbed the lead with spectacular strike from Goodwillie.
With the Derby defence on the back foot Goodwillie raced towards goal and curled home a powerful effort.
Ferguson's men have won only two of their last 24 games before this encounter, and by the 19th minute they were 3-1 down as Derby caused havoc down the Blackpool left.
The Rams equalised in the third minute when Johnny Russell glided past Blackpool right-back Tony McMahon and his low cross was turned into the net by Martin.
Derby's crisp passing and movement soon carved open the hosts backline and on-loan Chelsea striker Bamford added a second when he tapped in at the near post from Bryson's low cross.
Midfielder Bryson was a constant threat to the Blackpool defence and he notched Derby's third with a brilliant solo effort.
Bryson cut in from the left flank and with Blackpool goalkeeper Matt Gilks unsighted he curled a low shot into the bottom-left corner of the net.
Derby beat Blackpool 5-1 in the reverse fixture in December and with the Blackpool defence at sixes and sevens a similar scoreline looked ominous.
However, the home side showed a bit of fight immediately after the break and Grant produced a brilliant diving one-handed save to block Andy Keogh's close-range header.
Derby seemed content to soak up pressure and hit Blackpool on the counter attack and the Blackpool defence had to be on their toes on the hour mark.
Ferguson threw on Chris Basham and Tom Barkhuizen in a bid to freshen up his side in the final third and Blackpool exerted more pressure.
However, Derby's defence simply closed ranks and easily dealt with high balls aimed at Keogh as the hosts grew more frustrated.
With little to cheer on the pitch the home supporters turned their ire on Blackpool owner Karl Oyston in the remainder of the contest.
And there were ugly scenes towards the end as Tangerines fans clashed with stewards as they congregated in front of the stand where Oyston was sat to bemoan a side that are now only three points clear of the relegation zone.