Derby extended their unbeaten home run to nine matches but on this evidence the introduction of England's leading scorer Wayne Rooney to the playing squad in January cannot come soon enough, with the Rams taking 79 minutes to register a shot on target.
The visitors made the brighter start and almost went ahead after nine minutes when a Barry Bannan corner caused panic in the six-yard box and Malone had to divert the ball wide of the post with Fletcher lurking.
From the resulting set-piece, Curtis Davies produced a goal-saving tackle as Fletcher prepared to pull the trigger after the ball fell to him six yards out.
Wednesday took the lead midway through the first half. Fletcher put Craig Forsyth under pressure and the Derby defender's misplaced pass fell to Bannan, who found Fletcher 20 yards from goal and the Scotland striker's first-time finish nestled in the bottom corner.
Jason Knight fired Derby's only decent chance of the first half over the crossbar after a Duane Holmes long throw found him unmarked in the area, while the away side might have been out of sight but Ben Hamer tipped a Fletcher header over and from the subsequent corner Sam Hutchinson nodded narrowly over.
Derby should have been level moments after the interval but Martin headed Holmes' cross over from eight yards.
The Owls had a chance to extend their advantage after 55 minutes but Fletcher headed over from Adam Reach's right-wing cross.
At the other end Morgan Whittaker – making his first league start for the Rams – teed up Knight, only for the teenager to drag his 20-yard effort wide.
Fletcher's clever turn created an opening after 63 minutes but he shot straight at Hamer and Wednesday were made to pay for their spurned chances late on.
Substitute Jack Marriott was fouled in the box by Moses Odubajo and Martin converted the 82nd-minute penalty.
Odubajo was booked conceding the penalty and then given his marching orders for fouling Malone as Derby looked to break late on.
Derby almost capitalised to take all three points but a Tom Lawrence corner was deflected narrowly over the bar and Davies shot over from 20 yards.