The Rams broke the deadlock just over 10 minutes before half time when Jeff Hendrick drilled the ball into the bottom corner from 20 yards out.
Derby were able to double their advantage just before the break with another long-range effort, although Johnny Russell's looping finish appeared to take a deflection off Bryson.
Bryson had a chance to add a third with a free kick from 25 yards out following a foul on Russell, but his effort went just wide.
Barnsley managed to give themselves some late hope when Nick Proschwitz found space in the box to lash the ball in for the visitors.
However, the hosts had a chance to restore their two-goal cushion straight away when Conor Sammon was tripped in the box, giving Derby a penalty.
Russell stepped up to take the spot kick, looking for his second goal of the game, but Steele managed to stop his shot with a low dive to his left.
Both sides pressed late on as Barnsley pushed for an equaliser while Derby tried to make sure of the win, but Grant was able to deny Dale Jennings, while Bryson saw his late shot saved by Steele.
Despite the win, Derby are no longer able to secure automatic promotion with Burnley beating Wigan Athletic.
The result leaves Derby third in the table, while Barnsley stay in the relegation zone, four points from safety with just two games left to play.