Derby ruined Vitor Matos' first game in charge of Swansea with a 2-1 away victory.
Joe Ward and Lars-Jorgen Salvesen struck either side of the interval as Derby climbed into seventh place in the Championship.
There was late anxiety for the visitors after Ethan Galbraith's sweet finish, but it was a deserved sixth win in seven games for the in-form Rams.
Matos had only taken two training sessions after leaving Portuguese second-tier outfit Maritimo on Monday to succeed the sacked Alan Sheehan.
But Matos' challenge was laid out bare in front of him as Swansea subsided to a fourth successive league defeat, the Welsh club staying 20th and four points above the relegation zone.
Derby had won five in a row before letting a two-goal lead slip and losing 3-2 at home to Watford on Saturday, but those painful memories evaporated.
Jay Fulton made his first league start since the opening day of the season - and his 300th Swansea appearance - as Matos made four changes from the side overrun at Bristol City on Saturday.
Matos was so involved applauding an early attack that he strayed on to the touchline and was almost knocked to the floor by the assistant referee.
In truth, there was little to get excited about with Derby half-threatening through Sondre Langas and Patrick Agyemang and Swansea's top scorer Zan Vipotnik's goalbound effort striking team-mate Ronald and flying over.
Salvesen sent a header straight at home goalkeeper Lawrence Vigouroux, and Swansea's best moment came moments later when Eom Ji-sung cut inside for Jacob Zetterstrom to divert a shot heading into the bottom corner.
Swansea were grateful to Ben Cabango backheeling away Bobby Clark's cross into a packed goalmouth, but Derby punished slack marking from their next attack after 34 minutes.
Callum Elder's cross to the far post evaded everyone, including the sliding Agyemang, until Ward headed home his first league goal since April 2024.
Zetterstrom held an Eom header and Liam Cullen blazed over from 20 yards before Derby doubled their lead eight minutes after the break.
Cabango made a hash of Ward's cross and the unmarked Salvesen found the top corner from 14 yards.
The Swansea skipper's anguish continued after rising to meet Goncalo Franco's free-kick.
Cabango was only six yards from goal but his header went straight into Zetterstrom's midriff.
Ben Brereton-Diaz almost rubbed salt into Swansea wounds before Galbraith's fine strike set up a grandstand finish that eventually came to nothing.
Swansea's Vitor Matos:
"The result was not good, that's clear. In the game there were good moments that we can build from. I think that's the most important thing, that now we have a starting point to build from.
"We need to improve a lot of things, (that is) clear. The way we need to finish our attacks, the way we have the ball possession, we don't create the chances - that's what we need to improve."
Derby's John Eustace:
"We looked at how he (Matos) does things, we do things properly. Swansea play 4-3-3. and he's come from a team that played 4-3-3. So we expected 4-3-3.
"It was always going to be a very difficult night with the new manager coming in. It's a great three points.
"We ran out of steam against Watford (in a 3-2 defeat on Saturday), but I'm delighted with the response. That's what it was all about. We wanted the reaction."
