There was an early scare for the hosts when Fletcher raced clean through on goal in the second minute, almost scrambling the ball over the line by deflecting Rams goalkeeper Scott Carson's attempted clearance back at him.
The Rams enjoyed the lion's share of the early possession and piled bodies forward in the seventh minute, staging an attack which came to an end with Andreas Weimann slicing a half-volley over the bar.
A dangerous cross from Paddy McNair almost caught Carson out in the 10th minute and one of his teammates would surely have capitalised if the Derby keeper had not palmed the ball behind at full stretch.
Sunderland took the lead from the resulting corner, which fell kindly for Honeyman to strike, the midfielder finding the net with the help of a massive deflection off Rams defender Craig Forsyth.
The Black Cats headed into the match without a win in their last 10, but they gave themselves a great chance to end that dismal run of form in the 36th minute when Fletcher doubled their lead.
The striker latched on to a bad backpass from Derby skipper Richard Keogh around 30 yards from goal and used his pace to bear down on Carson, beating the home stopper with a low strike into the bottom corner.
Derby handed themselves a lifeline three minutes before half time when Matej Vydra found the net, the Czech striker smashing home his 18th of the campaign after Weimann had nodded Johnson's looping cross into his path.
Sunderland blew a gilt-edged opportunity to make it 3-1 in first-half stoppage time when McGeady's cross from wide on the left picked out an unmarked Fletcher in front of goal, but the forward sliced his shot wide of the post.
McGeady kept his cool to guide the ball beyond Carson, putting Sunderland on course for a shock win.
The former Everton winger linked up with Fletcher well in the 66th minute as his through-pass sent the striker clean through on goal, but his teammate could only find the woodwork when he unleashed a curling strike.
The visitors hit the frame of the goal again moments later when McNair's deflected header from a corner beat Carson but not the crossbar.
Chris Coleman's side, however, made the points safe in the 76th minute when O'Shea scrambled the ball over the line from close range after Lamine Kone had headed McNair's free kick invitingly across the face of goal.
The win moves Sunderland off the foot of the Championship table and above Burton Albion into 23rd, though they remain three points away from a position of safety.
Derby, meanwhile, missed out on the chance to cement their place in the playoff positions but remain in fifth.
DERBY COUNTY (4-2-3-1): Carson; Davies, Keogh, Forsyth, Baird; Vydra, Johnson, Thorne (Nugent 58'), Weimann, Lawrence (Palmer 45'); Jerome (Ledley 83')
SUNDERLAND (4-1-4-1): Camp; O'Shea, Kone, Love, Oviedo; (Matthews 81'); Cattermole; Honeyman, McNair (Wilson 78'), McGeady, Gooch (Maja 91'); Fletcher