It was evident from the start that Wednesday were intent on trying to subdue Derby's creative players with power and aggression.
Craig Bryson should have broken the deadlock with the home side's first real sight at goal, but missed the target from close range.
Wednesday goalkeeper Chris Kirkland was then called into action to keep out Hughes' strike, moments after Seyi Olofinjana had headed wide at the other end in the Yorkshire side's only real first-half opportunity.
The Rams continued to pile forward and Craig Forsyth headed wide from Jamie Ward's cross.
Derby's persistence was rewarded on the stroke of half-time aggression and it was ironic that Steve McClaren's inventive side finally broke through with a set-piece goal.
Ward's left-wing corner was met with a thumping header from Buxton, with the ball crashing in off the bar.
The second half began with renewed pressure from the home side, with another header from Buxton just clearing the bar.
Then Wednesday's defence were carved open four minutes after the re-start as a low cross from Craig Forsyth left England Under-21 international midfielder Hughes with a tap in from two yards at the far post.
Wednesday boss Dave Jones responded by bringing on Jermaine Johnson and Giles Coke and the former almost had an instant impact.
Johnson sprinted clear on the right to fire in a dangerous low cross but a rare chance for the Owls went begging as Michail Antonio blazed his shot into the stand.
Derby were much more clinical when they swept up-field to score a third goal in the 58th minute, which effectively ended any chance of comeback.
Ward provided the cross from the right and the impressive Martin slotted home from point-blank range for his fifth goal in the Championship and eighth in all competitions.
Johnson nearly got the visitors back into the contest but blazed over, while Derby looked to make an emphatic statement.
Simon Dawkins missed the target, Martin was denied a second by an important block from Wednesday defender Roger Johnson, while Matt Fryatt headed wide.
Kirkland prevented Ward from getting a deserved goal by pushing away an effort from the striker, while at the other end Lee Grant kept his goal in tact with a fantastic save from point-blank range from Wednesday's on-loan striker Connor Wickham.