Nigel Clough's side move level on points at the top of the Championship with early season pacesetters Southampton and Brighton after a result which marks the first time Derby have started the league season with three consecutive wins since 1948.
Blackpool - who also boasted two wins out of two before the game - controlled possession for long periods, but despite the persistent menace of Gary Taylor-Fletcher in attack they were unable to find a way through a stubborn Derby backline.
After an uneventful opening period, Derby's Jamie Ward came agonisingly close to opening the scoring when he curled the ball on to the woodwork from 25 yards.
The decisive moment came midway through the half, with Bryson pouncing after Blackpool goalkeeper Matt Gilks failed to push Steven Davies' free kick to safety.
Centre back Matt Hill replaced Craig Cathcart in the only change to the Blackpool XI that started the season's opening two league encounters.
Ward recovered from a hamstring problem to take Lee Croft's place in the Derby line-up Five minutes into a scrappy opening Blackpool's Elliot Grandin switched play to the right flank, finding Taylor-Fletcher lurking and the forward's cross flashed dangerously across the Derby goalmouth.
At the other end Steven Davies released Bryson down the right channel and his cutback narrowly evaded the onrushing Ward.
A 25-yard Taylor-Fletcher drive brought the first save of the match in the 22nd minute - England Under-21 goalkeeper Frank Fielding tumbling to his right to hold comfortably.
Ben Davies cut in from the right flank for Derby's first attempt three minutes later but dragged a tame shot wide. The same player then saw Gilks claw his goalbound cross to safety.
The rest of the half passed off with little incident, but on the stroke of the interval, Taylor-Fletcher and Kevin Phillips combined cleverly on the edge of the Derby area where the latter played in Stephen Crainey.
The full-back's shot was deflected narrowly wide and from the resulting corner, Keith Southern volleyed into Fielding's arms.
Taylor-Fletcher again provided Blackpool's main threat at the start of the second half as he danced through a pair of Derby challenges before teeing up Phillips to drill wide.
Ward almost illuminated the contest with an hour gone when he uncorked a curling, dipping effort on to the angle of post and bar with Gilks rooted to the spot.
Blackpool responded by peppering the Derby box with a succession of crosses and corners, but a Rams defence impressively marshalled by skipper Jason Shackell stood firm.
The hosts were starting to look a touch ragged in defence, conceding free-kicks in dangerous areas, and when Hill bundled Steven Davies over in the 68th minute it proved to be their undoing.
Gilks plunged to his right to keep out the same player's well struck 25-yard effort, but could only parry as far as Bryson who slotted home.
Predictably, Taylor-Fletcher authored the Blackpool response, engineering space in the area before firing narrowly wide.
A final chance came Blackpool's way, but Southern blazed past the post after Phillips failed to control a cross from substitute Billy Clarke.