The Whites dominated the 1st-half in impressive fashion and deservedly led after Stuart Dallas fed Tom Adeyemi to head home his first goal for the club two minutes before the interval.
But Derby began the second half like a rocket, equalising through Chris Martin just three minutes after the break, but Leeds dealt a deadly sting in the tail through Wood’s pearler just two minutes from normal time.
It must have been a close call between Mowatt and Luke Murphy for that particular midfield role alongside Adeyemi who kept his place and Cook.
There was also no place on the bench for striker Lee Erwin with Souleymane Doukara preferred.
And despite an intimidating home atmosphere, United began brightly with Cook, Mowatt and Sam Byram all linking up to feed Wood who fired just over from the edge of the area.
Derby hit back with an attack down the left flank in which Craig Forsyth’s touch let him down before play was interrupted as Cook accidentally caught Richard Keogh in the face with his studs without picking up a booking.
Keogh returned with his head bandaged and it was Leeds who then did the pressing with a series of promising attacks and corners ended as Dallas fired over from range.
Leeds continued to push forward with only a poor first touch from Dallas ended a threatening move down the left but a few minutes later a left flank Jonny Russell cross caused panic in the Whites area before Bamba was on hand to clear.
The Rams then forced a corner from which Byram had to practically clear off the line before Bamba was on hand to clear another Rams foray for another corner.
That set piece was also dealt with but Gaetano Berardi then clattered into Forsyth on the left flank resulting in a free-kick from which Martin’s glancing header went just wide.
But Leeds responded with the impressive Cook released down the right hand side with the midfielder running some 30 yards before forcing a corner.
Mowatt’s delivery wasn’t the best but the move still ended with a half chance for Cook who fired over from an angle.
Even Liam Cooper then posed an attacking threat as his adventurous run and fine pass narrowly failed to find Wood’s outstretched boot.
And United’s consistent pressure brought rich dividends two minutes before the break when a left flank corner was worked to Dallas whose fine cross found Adeyemi to produce a clinical headed finish.
The goal was no more than Leeds deserved and with Derby rattled the Whites so nearly bagged a second.
Mowatt fed the energetic Cook on the right wing and the teenager’s dangerous cross was desperately parried away by former Leeds stopper Scott Carson.
Even then, United went on to force another corner - their sixth of the half - and while the Rams cleared, the half-time whistle brought a chorus of boos from the home faithful at the iPro.
There were no changes at the interval and, as expected, Derby began the second half with a bang.
Tom Ince immediately fed Russell who fired over from the edge of the area before Marco Silvestri was called into making a tremendous one-handed save to turn Jeff Hendrick’s effort over.
But just one minute later there was nothing Silvestri could do to stop Martin’s clinical finish from the edge of the area which nestled into the bottom corner, the striker turning Cooper before coolly making it 1-1 three minutes into the second half.
Derby had started the half like a house on fire - raising the roof of the iPro - and Hendrick so nearly gave the Rams a 55th minute lead with his effort from the edge of the area whistling just wide of Silvestri’s right-hand post.
A brief Mowatt run offered Leeds some welcome respite but the midfielder opted not to shoot from his usual range and the Rams were soon back on top with Russell firing wide from 25-yards.
Derby were in control and amidst a brief pause for breath, Rams boss Paul Clement opted to bring on Andreas Weimann for Thorne with 25 minutes remaining.
And just two minutes later United were again left thanking Silvestri for another fine diving save to keep out the effort of Russell which went for a corner.
Leeds cleared but it was one-way traffic and Rosler reached for Murphy in place of the once-again subdued Byram after 69 minutes.
Hendrick then picked up the game’s first yellow card for his late challenge on Adeyemi after 71 minutes but the Rams were soon back causing panic with a flowing counter attack ending with strong claims for a penalty amidst Cooper’s crucial interception.
An animated Rosler reacted by bringing on Mirco Antenucci for Mowatt with 15 minutes remaining and almost immediately Antenucci set up United’s best chance of the half.
His raking cross from the left wing found Wood with a free header inside the penalty area but the striker could only put his effort over the bar.
With 11 minutes remaining, Clement introduced Darren Bent for Russell but Bent looked out of sorts as the anticipated late home onslaught failed to materialise.
And just when the game appeared to be meandering towards another draw, up popped Wood with an absolute gem on 88 minutes.
From nothing, the striker worked himself the opportunity for a shot from 20-yards out and curled a stunning effort which Carson could only watch like a statue as the ball sailed into the far-right corner.
The effort left the home faithful stunned as some headed for the exits but five minutes of injury time gave them hope.
But this time there was to be no late collapse from the Whites who saw out added time in impressive fashion to land an impressive first win of the campaign.
Derby County: Carson, Forsyth, Keogh, Hendrick, Martin, Russell (Bent 81), Baird, Shackell, Ince, Hanson (Shotton 86), Thorne (Weimann 65). Subs not used: Grant, Dawkins, Pearce, Warnock.
Leeds United: Silvestri, Berardi, Cooper, Bamba, Taylor, Adeyemi, Cook, Mowatt (Antenucci 75), Byram (Murphy 69), Dallas, Wood. Subs not used: Turnbull, Wootton, Bellusci, Phillips, Doukara.
Referee: Darren Bond (Lancashire).
Attendance: 29,386 (2,335 Leeds).