Goals from Gwion Edwards and Freddie Sears have given Town a 2-1 half-time lead over Swansea, the home side having gone in front early on via a Cole Skuse own goal.
Edwards, Sears, Matthew Pennington and Andre Dozzell all started for the Blues with Jonas Knudsen, Jon Nolan, Kayden Jackson and Jordan Graham dropping to the bench having been in the XI which lost 2-0 to Middlesbrough on Tuesday.
Knudsen’s usual left-back role went to Janoi Donacien, who moved from right-back with Matthew Pennington returning after his one-match ban.
Skipper Luke Chambers and Toto Nsiala continued at the centre of the defence in front of keeper Dean Gerken.
Cole Skuse and Trevoh Chalobah were in their usual deeper midfield roles with Dozzell, making his first start since the opening day of last season, coming in for Nolan ahead of them.
Edwards, facing the club where he came through the youth ranks, was on the right with Grant Ward on the left and Freddie Sears the lone striker.
Young striker Jack Lankester was on the bench for the senior side in a competitive fixture for the first time having been handed the number 36 shirt. Another academy product, left-back Bailey Clements, also made the trip to Wales but didn’t make the final 18.
Former Blues loanee Bersant Celina started for the Swans, while another of last season’s Town loan players, Cameron Carter-Vickers, was among their subs.
The home side threatened in the opening seconds, Town having lost the ball soon after kicking off. Dan James broke into the left of the box and hit a shot which Gerken blocked. Connor Roberts was unable to divert the rebound goalwards.
Town threatened for the first time in the third minute, Dozzell threading a pass through for Sears, who beat the offside trap and was in on goal. However, the ball seemed to get stuck under the former Colchester man’s feet and he was caught by Joe Rodon, who stabbed behind for a corner.
Aside from that chance - and it was a very decent opportunity - the early stages were dominated by Swansea and in the ninth minute they went in front via a Skuse own goal.
James sent a ball across the six-yard box from the left following a one-two with Celina which Oli McBurnie failed to reach. But Roberts crossed back in from the right and the ball beat Gerken off Skuse.
Ward shot from distance for Town on 10 but without significantly troubling Kristoffer Nordfeldt in the Swans goal.
Sears was subsequently sent away down the right channel and won a corner, Nsiala just failing to connect with a far-post header. Soon after, the former West Ham man broke away again but chipped his cross over the bar with his options in the box limited in any case.
On 20 the lively James again burst away behind the Blues’ backline on the left and as previously McBurnie was just unable to get a touch on his low cross.
James was giving Pennington a tough time and four minutes later he escaped again before cutting back to Celina, who fortunately for the Blues screwed his shot well wide.
It had been all Swansea but in the 27th minute Town equalised via former Swan and local boy Edwards. Sears crossed superbly from the left and the winger nodded across Nordfeldt and into the net from a few yards out.
Four minutes later, the same pair combined in reverse to hand the Blues a lead which had looked hugely unlikely only moments earlier.
Sears fed Edwards on the right and broke forward into the area before flicking the Welshman’s ball into the box across Nordfeldt, although Swans skipper Van der Hoorn may have got the final touch. Nevertheless Sears celebrated and will presumably claim his first goal of the season.
Shocked Swansea went about trying to restore parity and went close in the 35th minute. Celina was sent away on the right of the box and played inside to McBurnie. The Scotland international cut past Pennington but was thwarted by Gerken who came out quickly to block his shot.
The Blues briefly found themselves under pressure but on 42 weren’t too far from a third. Edwards broke away down the right and sent the ball across the six-yard box but just too far in front of Sears.
Town ended the half with their lead still intact and with the Swans having continued to dominate possession but without creating a further chance.
The home side will have gone in scratching their heads wondering quite how they found themselves behind.
They had completely dominated the early stages and scored the early goal which ought to have seen them on the way to a comfortable half-time lead.
However, they were unable to profit from their advantage and Town twice caught them with a sucker punch with Sears and Edwards having created problems on the break all half and the Blues might even have added a third late on.
As at Birmingham last Saturday, Town have a big 45 minutes ahead as they again look to end their long wait for their first win of the season, a victory which might even save manager Hurst’s job.
Swansea: Nordfeldt, Van der Hoorn,, McBurnie, Celina, Carroll, James, Grimes, Rodon, Roberts, Naughton, Byers. Subs: Mulder, Olsson, Fer, Asoro, Carter-Vickers, McKay, Fulton.
Town: Gerken, Pennington, Nsiala, Chambers (c), Donacien, Skuse, Chalobah, Edwards, Dozzell, Ward, Sears. Subs: Bialkowski, Knudsen, Jackson, Nolan, Graham, Downes, Lankester. Referee: Oliver Langford (West Midlands).