Swansea - who travel to Barnsley on Saturday - moved second after Darren Pratley's 43rd-minute opener and a second-half penalty brace from Scott Sinclair against struggling Palace.
Swans boss Brendan Rodgers said: "Palace worked very hard and made it difficult for us but we played very well. We pressed the ball from the first minute and we showed creativity and imagination in the final third."
Opposite number Dougie Freedman did not flinch from the size of the challenge facing him with his side third bottom. He said: "We are in the bottom three and have been there for most of the season. It is the most difficult challenge of my life."
Russell Martin scored deep into injury time as Norwich salvaged a 1-1 draw against Cardiff at Carrow Road after Jon Parkin appeared to have won it for the Bluebirds.
Canaries boss Paul Lambert said: "I thought we were excellent, I really did, against a really good side.
"It would have been very tough on us if we hadn't got anything from the game."
Cardiff counterpart Dave Jones accepted a draw was a fair result, saying: "I didn't actually think it was a goal at first but overall it was probably a fair result on the day."
Sanchez Watt, Max Gradel, Bradley Johnson and Davide Somma condemned struggling Scunthorpe to a 4-0 defeat, with Leeds now level on points in fifth with Cardiff and Norwich.Leeds boss Simon Grayson said: "When you go 3-0 up with early goals it gives you a platform to win, but we did the other side of the game really well. We knew it was going to be a tough game against Scunthorpe, who are fighting for their lives. We knew they'd work hard and close us down but we did that to them."
Watford are sixth after a 3-0 win over Derby thanks to Will Buckley, Danny Graham and Marvin Sordell, their sixth league win in a row.
Nottingham Forest are eighth, behind the Royals on goal difference, after a 2-1 win over Portsmouth.
Kanu put Pompey ahead but an 87th-minute Ibrahima Sonko own goal levelled matters before Marcus Tudgay netted in the final minute of injury time.
Millwall beat struggling Ipswich 2-1 in Paul Jewell's first game as manager and Middlesbrough also inched away from trouble with a thumping 4-0 win at Bristol City.
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