Brendan Rodgers' side edged the first half but struggled to break down a resolute Derby defence in a disappointing encounter.
Stephen Dobbie twice came close for the Welsh side and Craig Beattie had two late chances to win it, while Derby also had their chances in the second half but the game always looked destined to finish goalless.
A point for Derby stretched their unbeaten run to three matches but Nigel Clough's side are without a win on their travels since the opening day of the season.
The Swans were without leading scorer Scott Sinclair and influential midfielder Darren Pratley due to injury.
Clough was forced into one change from the side that beat Middlesbrough in midweek with Shefki Kuqi ineligible to face his parent club, so Luke Moore was handed a first start since his loan move from West Brom.
Dobbie had an early chance to put the home side in front but the striker headed over the crossbar from six yards out after being picked out by Andrea Orlandi.
Swans central defender Ashley Williams should have done better when he rose to meet Mark Gower's outswinging corner but headed over the bar.
But Derby started to get into their stride and the in-form Kris Commons tested Dorus De Vries with a shot from just outside the penalty area, but the Dutchman saved comfortably.
Dobbie came close to opening the scoring 10 minutes before half-time but Stephen Bywater dived to tip his left-foot strike from the edge of the penalty area around the post.
Derby were dealt a blow early in the second half when Commons sustained an injury, with Ben Pringle replacing the tricky forward.
Swans boss Rodgers brought on recent loan signing Frank Nouble to add an extra dimension to their attack.
But Derby should have broken the deadlock after 67 minutes when substitute Stephen Pearson fired over the bar from close range.
Central defender Shaun Barker rose highest to meet Pringle's inswinging corner but the former Blackpool man headed over the bar with 17 minutes remaining.
Swansea had a good chance to win it six minutes from time when John Brayford upended Nathan Dyer and from the resulting free-kick Jordi Lopez crossed for Alan Tate, but the defender fired over the bar from just six yards out.
Beattie had two good chances to snatch all three points late on but Derby held on for a hard-earned point.