Marcelo Bielsa's Leeds side will face Derby County in the Championship play-off semi-final
Leeds United stuttered their way into the play-offs as relegated Ipswich picked up a rare victory.
Collin Quaner grabbed a 90th-minute winner for the Championship's bottom club moments after they had been reduced to 10 men.
Ipswich had earlier led twice through strikes from Flynn Downes and Andre Dozzell either side of goals from Mateusz Klich and Stuart Dallas.
Leeds spurned the chance for victory themselves when Kemar Roofe failed to convert a penalty awarded to him by a foul from Luke Chambers, which saw the Ipswich captain sent off.
Marcelo Bielsa's side held on to third place despite the defeat and will now face Derby County in the play-off semi-finals, who finished sixth with victory against West Brom.
But Leeds will go into that tie on a four-match winless run after three defeats in their last four regular season fixtures.
Ipswich's win was just their fifth of a torrid campaign, with Quaner's late goal ensuring they scored three at home for the first time this season.
Downes' first senior goal on the half-volley fired them into the lead when Leeds failed to clear an Alan Judge free-kick from the right.
Leeds levelled on the stroke of half-time when Klich lashed in a ball from Luke Ayling into the bottom corner.
Ipswich were back in front moments after the restart when Dozzell calmly finished left-footed from Quaner's ball into space for his first goal since his debut at the age of 16.
After concerted Leeds pressure, Dallas equalised again when Roofe's header off the crossbar rebounded into his path.
But Roofe then failed to convert what would have been the winner from the spot and there was still time for Quaner to take advantage of a defensive mix-up between Kiko Casilla and Ayling to sweep the loose ball into an empty net.
Ipswich Town manager Paul Lambert:
"It was a brilliant, but that's what we have deserved. With all the draws we've had, if we'd won another six, I don't think anyone would have begrudged it.
"It's only the last three games or so that the wind was taken out of our sails. I can't ask for anything more. We always looked dangerous.
"Leeds United are a very good side and not many teams have beaten them. We got the breaks at the right moments. We played some good, energetic football."
Leeds United manager Marcelo Bielsa:
"If you put aside the mistakes we made from this game, the performance from the team was good enough.
"At the end of the game you could not think that this opponent could score three goals against us and it was impossible that we could not score three or four goals.
"We conceded three goals and this is something that is honestly impossible to explain and we also only scored two goals, which is also difficult to justify."
