But manager Roberto Martinez not giving up on slim hopes of staying up in top-flight next year. And Manchester City beat West Brom.
English football round-up: Defeat puts Wigan in further trouble
The league's perennial escapologists, Wigan would have clambered out of the bottom three with a win but defensive howlers led to Swansea striker Itay Shechter making it 2-2 in the 59th minute and Dwight Tiendalli grabbing a scrappy winner in the 76th.
Wigan are three points from safety with games to come against Arsenal away and Aston Villa at home. They have escaped relegation on the final day in three of the last six seasons but this could be a step too far.
"We have done it before and we can do it again - we can go anywhere in the Premier League and get the points," Wigan manager Roberto Martinez said.
The hosts had twice taken the lead at DW Stadium, through Roger Espinoza with the last kick of the first half and then James McCarthy in the 53rd, canceling out Angel Rangel's equaliser three minutes earlier.
Newcastle, Norwich and Sunderland, who are all three points clear of Wigan, as well as a host of other clubs above them will have breathed a big sigh of relief when referee Kevin Friend blew for full time after nine minutes of injury time following a serious-looking injury to Swansea goalkeeper Michel Vorm. The Netherlands international was carried off on a stretcher late on after clashing with teammate Ben Davies in an aerial collision but Michael Laudrup, the Swansea manager, said Vorm was not seriously injured.
Wigan has an FA Cup final to look forward to against Manchester City on Saturday but survival in England's lucrative top division is always the priority. The Latics could yet need to beat Arsenal on Tuesday to have a chance of staying in the Premier League for a ninth straight season.
"There are still many twists and turns," Martinez said. "Obviously today was a fantastic opportunity ... but it doesn't change the fact we have to fight for every single point."
"Ain't No Mountain High Enough" blared out around DW Stadium as the players warmed up, and fans heartily sang "I'm A Believer" as the match kicked off. They know in these parts that Wigan's season does not really get going until April - while nerves are jangling across much of the Premier League heading into the final week of the campaign, Martinez and his players are usually at home in this pressurized environment.
Tension got the better of them in an end-to-end second half marked by careless passing and defensive errors, allowing Swansea to come away with all three points when it looked dead and buried at halftime after a lackluster display and Espinoza's volleyed goal in stoppage time.
"It's frustrating the way the match developed," Martinez said. "You have to accept we shot ourselves in the foot."
Dzeko goal hands Manchester City win
The Bosnian, whose double at The Hawthorns in October included a last-gasp winner, guided home a volley after 35 minutes of a Premier League clash lacking in intensity but not incident.
Both sides spurned numerous chances with City hitting the woodwork twice through Carlos Tevez and James Milner in the first half and Marcus Rosenborg doing likewise for West Brom after the break.
Benitez defends 'dying swan' Luiz
Rafael Benitez, the Chelsea interim manager, has launched a vigorous defence of David Luiz after Sir Alex Ferguson accused the Brazilian of acting like a "dying swan".
Luiz has established himself as a key player in the Chelsea Champions League-chasing side which secured a 1-0 Premier League win at Old Trafford on Sunday, but has been criticised for his role in the dismissal of his Brazil teammate Rafael.
After being kicked by Rafael, Luiz was seen on the ground and smiling - his defence was that his smile was as a result of supporters' taunts over his likeness to The Simpsons character Sideshow Bob, who also has a mop of curly brown hair.
Luiz will not face any action from the English Football Association over the incident.
Asked if he was aware who Sideshow Bob is, Benitez said: "I'm aware David Luiz is one of the best players in the Premier League, by miles - miles away from a lot of players. He's one of the best, without doubt.
"David Luiz was laughing because the fans were abusing him. After was the red card [for Rafael]. It was very clear, the timing.
"If we continue talking about this, instead of trying to eradicate the bad tackles that you can see every week, I think we're giving importance to something that is not as important."
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