The Rams were up against it for large parts but when Wednesday were unable to break the deadlock, Bamford showed them how to do it in style.
With 12 minutes remaining, the Chelsea loanee curled in a wicked effort from 20 yards to register his fifth goal in six games and earn a 1-0 win.
The success kept Derby's hopes of automatic promotion firmly intact as they moved to within two points of second-placed Burnley.
It was harsh on Wednesday, who for the second game running were made to pay for a stack of missed chances, with Michail Antonio denied by Lee Grant on three occasions.
In fact, Wednesday were on top from the start, though there was little to get the pulse racing in the opening 20 minutes, with Glenn Loovens' header, which was cleared off the line by Craig Bryson, the best effort.
Derby eventually began to stir and highly-rated midfielder Will Hughes in particular became influential.
Hughes was pulling all the strings and created a great chance when he danced through the Wednesday defence, but elected to shoot when Jamie Ward was far better placed and his weak effort was easily saved by Chris Kirkland.
Antonio was Wednesday's most dangerous player in the first half and he again proved a threat early after the restart when he cut in and forced Grant into a smart save down to his left.
The former Reading winger was back in the action soon after, forcing a corner from which a dominant home side almost took the lead.
After Wigan's Martyn Waghorn scored direct from a corner against them last week, the Owls almost achieved the feat themselves as it needed a desperate clearance from Bryson on the line to hack away Chris Maguire's low delivery.
Antonio was central to what Stuart Gray's men were doing as he further tested Grant on two occasions, first with a low effort and then one that the former Wednesday keeper did well to hold on to from 18 yards.
The longer the hosts went without being able to make the dominance count, the more it seemed as if they would pay at the other end and so it proved in the 76th minute.
On a rare foray forward Derby worked the ball out to the left where Andre Wisdom poked it back to Bamford and the on-loan Chelsea man curled a superb 20-yard effort from the angle of the penalty area which crashed in off the underside of the bar.
It was a stunning goal and it needed something like that for the Rams to make a mark on the game.
It made for a frantic final 15 minutes, but Derby held on to highlight their promotion credentials.