Shefki Kuqi headed the Swans to an important victory in a fiery game at Pride Park.
The Finnish international striker connected with David Cotterill's free-kick just after the hour to score his second goal since arriving in south west Wales last month.
Derby had Jay McEveley sent off after he grounded Nathan Dyer which led to the free-kick being awarded but the Swans were also reduced to 10 when substitute Gorka Pintado was dismissed for a challenge on Robbie Savage.
Garry Monk missed out at Derby with a back injury sustained before the team departed for the east Midlands on Friday.
The Swans captain was replaced in defence by Ashley Williams, who played the last game in midfield, while youngster Jazz Richards continued at left-back.
Joe Allen, Nathan Dyer and David Cotterill all returned to midfield with Ferrie Bodde named amongst the substitutes for the first time since his return from injury.
Derby: Stephen Bywater; Jay McEveley, Shaun Barker, Jake Buxton, Nicky Hunt, Stephen Pearson (Dean Moxey, 90+1'), Robbie Savage (C), Michael Tonge, Paul Green, Kris Commons (Gilles Sunu, 25'(Chris Porter, 85')), Rob Hulse.
Subs: Saul Deeney, Ben Pringle, David Martin, Russell Anderson.
Swans:Dorus de Vries; Angel Rangel, Alan Tate(C), Ashley Williams, Jazz Richards; Joe Allen (Gorka Pintado, 63'), Andrea Orlandi (Mark Gower, 15'), Darren Pratley, Nathan Dyer (Tom Butler, 87'), David Cotterill; Shefki Kuqi.
Not Used:David Cornell (GK), Ferrie Bodde, Lee Trundle, Besian Idrizaj.
Attendance: 31,024 Away: 1,407
Referee: S Tanner (Avon)
The home side for this contest underway and were immediately on the offensive with Rob Hulse and former Wales international Robbie Savage handing out the early warning signs.
But it was Rams' goalkeeper Stephen Bywater who was the first of the two goalkeepers called into action when he was handed the simple task of saving Darren Pratley's close-range header on three minutes.
Paulo's side held the advantage early on as they delivered two dangerous balls into Derby's area but Rob Hulse completed a sweeping move by forcing Dorus de Vries into stopping the striker from close-range.
They came close again moments later through Kris Commons whose right-footed drive deflected wide of goal for a corner.
The Swans responded with a sweeping, counter attacking move of their own with Pratley and Nathan Dyer teeing up Shefki Kuqi to shoot straight at Bywater, of which came after Andrea Orlandi's departure from this fixture because of a hamstring injury; the Spanish midfielder was replaced by Mark Gower.
Both sides seemed to be cancelling eachother out as the half went on while the Rams were also forced into making their first change with Kris Commons going off to be replaced by Gilles Sunu.
If anything Nigel Clough's side were edging it as far as attacking threat was concerned, and just before the half-hour de Vries was able to powerfully punch away a Michael Tonge corner which landed at the feet of Nicky Hunt who let fly to send his effort high into the stand.
Jay McEveley was even handed a chance from a dangerous free-kick which, fortunately, ended up in the stand while down at the other end Shefki Kuqi was unlucky not to latch on to David Cotteril's through ball shortly before the break.
Dorus was called into action again to deny a low drive from Tonge but the Swans held on to keep the scoreline goalless at the break.
Half-Time: Derby 0 Swans 0
The Swans did come out looking stronger at the start of the second-half and for the first five minutes looked to get into good positions in and around Derby's half.
A few heavy challenges did start to fly in with Nathan Dyer grounding Jay McEveley before the latter was booked for a wicked lunge on Joe Allen.
Both challenges certainly lifted the atmosphere inside Pride Park but both sets of supporters had to wait until the hour mark before a goalkeeper was even tested - in this instance it was Dorus de Vries who had to get down to deny Paul Green from 20-yards out.
The Swans suffered another blow moments later when Joe Allen was the latest player to go off injured, the young midfielder was replaced by Gorka Pintado just before this game started to come alive.
Derby left-back McEveley was booked just minutes before committing another foul to ground Nathan Dyer near to the right-hand touchline which referee Steve Tanner deemed to be another bookable offence - the Somerset official then branded the red card before David Cotterill placed the ball to deliver the set-piece into the area.
The winger delivered an excellent ball into the area which saw Shefki Kuqi connect with his head, guiding the ball past the 'keeper and into the bottom corner of the net.
But the drama didn't stop there, within a few minutes of the opening goal Mr. Tanner had his cards out again following a rash challenge by substitute Gorka Pintado on Robbie Savage, the Spanish front-man seeing red with both sides reduced to 10 men.
Normal order was restored with the home side looking for a way back into this game but the 10-man Swans combated well with the Rams' pressure.
Paulo's side still committed men forward to try and find a second and with five minutes remaining Darren Pratley flashed a header wide from a Cotterill corner.
The Swans still needed a bit of luck, and with two minutes remaining they got that luck when Michael Tonge struck the crossbar with an 88th minute free-kick while the follow-up was blazed high and wide by Chris Barker.
The visitors had to endure a painful six minutes of injury-time at the end of this match but hold on they did, registering an important 1-0 victory to keep their fourth-spot place in the Championship table.