Match ends, Swansea City 2, Ipswich Town 3.
Ipswich Town secured a first win of the season after Trevoh Chalobah's late goal at the Liberty Stadium eased the pressure on under-fire boss Paul Hurst.
Swansea had made the perfect start when Connor Roberts' cross was deflected in on eight minutes by Janoi Donacien.
Ipswich scored twice in four first-half minutes with Gwion Edwards levelling before Mike van der Hoorn's own goal.
Bersant Celina looked to have rescued a point for Swansea after a superb team move, only for Chalobah to head home.
Swansea started the contest strongly on the front foot and will wonder how on earth they lost a contest they dominated for long spells.
Daniel James might have given them the lead inside 60 seconds, but his charge into the box ended with Dean Gerken spreading himself to save as James fired left footed across goal.
The Swans' fast start seemed destined to pay sooner rather than later with Ipswich's confidence fragile and on eight minutes they found the breakthrough.
The goal was a simple one, another fast breakaway allowing Roberts time to pick out a cross that deflected in off former Newport County loanee Donacien.
Swansea should have extended their advantage in a period of real dominance, with Wales Under-21 winger James particularly catching the eye.
James twice flashed balls across the penalty area that just evaded Oli McBurnie and then helped to set the Scotland striker clear on 34 minutes, only to be denied by a point-blank save by Gerken.
However, by then it was a different match with the Tractor Boys somehow in front following two goals in quick succession as Swansea paid the price for switching off.
The goals were almost a carbon copy of one another, with Sears crossing for Edwards to head home on 27 minutes.
Edwards then returned the favour, with Sears' effort deflecting off Swansea skipper Van der Hoorn and evading Kristoffer Nordfeldt.
The Swans were within centimetres of levelling on 54 minutes, but Joe Rodon's header from a corner cannoned back off the crossbar, with Van der Hoorn heading the rebound agonisingly over.
James again crossed brilliantly with the ball evading everyone as Swansea chased an equaliser, which eventually came with just over 10 minutes remaining.
The goal was a stunning one, with the Swans sweeping the ball from their own penalty area, with sub Leroy Fer leading the charge.
The ball was eventually collected by Celina who fired low into the corner to seemingly earn the Swans a point against his old club.
However, the sting in the tail arrived when Chalobah headed home Grant Ward's corner.
Swansea could still have secured a point, but McBurnie headed wide and sub Joel Asoro missed the target after Tom Carroll's smart pass as Ipswich held on to move off the foot of the Championship.
Swansea City manager Graham Potter said:
"It was a crazy game. We started really well, got a good goal and pushed and pushed for a second.
"We conceded from not too much and it knocked us back.
"If you concede three goals you can't win football matches. We are disappointed, because we did a lot of things well.
"We have picked up some points where we have been fortunate but in the last two games we have played really well and picked up one point."
Ipswich Town manager Paul Hurst said:
"A win has been a long time coming and was unexpected coming here today - we were big underdogs, especially going 1-0 down.
"Swansea are a very good team and caused us, and other teams, a lot of problems.
"They played well and will be disappointed their final ball or final shot let them down.
"We had to ride our luck but we have not had much (luck), so I am not going to complain about that."
- 26NaughtonSubstituted forAsoroat 45'minutes
- 5van der HoornSubstituted forMcKayat 75'minutes
- 22RodonBooked at 88mins
- 28ByersSubstituted forFerat 58'minutes
- 2DonacienSubstituted forKnudsenat 45'minutes
- 6ChalobahBooked at 81mins
- 7EdwardsSubstituted forJacksonat 90+3'minutes
- 23DozzellBooked at 68minsSubstituted forDownesat 80'minutes
- Oliver Langford
- Shots on Target
Second Half ends, Swansea City 2, Ipswich Town 3.
Attempt blocked. Bersant Celina (Swansea City) right footed shot from outside the box is blocked. Assisted by Connor Roberts.
Corner, Ipswich Town. Conceded by Matt Grimes.
Attempt missed. Freddie Sears (Ipswich Town) left footed shot from the centre of the box misses to the left. Assisted by Kayden Jackson.
Attempt missed. Barrie McKay (Swansea City) right footed shot from outside the box misses to the right.
Substitution, Ipswich Town. Kayden Jackson replaces Gwion Edwards.
Attempt blocked. Bersant Celina (Swansea City) right footed shot from outside the box is blocked. Assisted by Tom Carroll.
Corner, Swansea City. Conceded by Jonas Knudsen.
Oliver McBurnie (Swansea City) wins a free kick in the attacking half.
Foul by Aristote Nsiala (Ipswich Town).
Joe Rodon (Swansea City) is shown the yellow card for a bad foul.
Foul by Joe Rodon (Swansea City).
Freddie Sears (Ipswich Town) wins a free kick in the defensive half.
Corner, Swansea City. Conceded by Cole Skuse.
Attempt blocked. Oliver McBurnie (Swansea City) header from the centre of the box is blocked. Assisted by Connor Roberts with a cross.
Attempt missed. Joel Asoro (Swansea City) right footed shot from the centre of the box is close, but misses to the right. Assisted by Tom Carroll.
Goal! Swansea City 2, Ipswich Town 3. Trevoh Chalobah (Ipswich Town) header from the centre of the box to the bottom right corner. Assisted by Grant Ward with a cross following a corner.
Corner, Ipswich Town. Conceded by Matt Grimes.
Corner, Ipswich Town. Conceded by Leroy Fer.