The Tigers dominated proceedings and deservedly took all three points thanks to a double from the Senegal international after wasting a host of chances.
N’Doye, the January signing from Lokomotiv Moscow, could - and really should - have had a hat-trick or more.
He was, though, in the right place at the right time to net twice after the restart to seal not only a first win at Selhurst Park in almost 30 yards but also a first triumph in the Premier League since mid-February.
With five games remaining - four of which are at home - City have now given their survival hopes a massive fillip ahead of Tuesday’s clash against Liverpool at the KC.
Both teams had a huge let-off inside the first 15 minutes. Hull’s came first, as James Chester getting the ball stuck under his feet presented a chance to Glenn Murray who fired the ball goalwards but was denied by Steve Harper.
It was a big let-off for the visitors and one they really should have capitalised upon when Robbie Brady picked out Dame N’Doye.
The Senegal international merely had to touch the ball past Julian Speroni from four yards but, somehow, managed to divert it away from goal and to safety.
Hull also went close on 21 minutes when Tom Huddlestone curled an effort that Julian Speroni did brilliantly to claw away from goal at full stretch.
It came moments after Sone Aluko had a big appeal for a penalty against Damien Delaney for handball waved away by referee Mark Clattenburg to underline just how well the visitors had started the game.
Just before the half-hour, Harper was called into action at the other end for the Tigers to deny Wilfried Zaha after the former Manchester United man had been played inside Robbie Brady by Jason Puncheon.
But it was City who finished the first half on top, as Jake Livermore wasted a great opportunity by firing straight at Speroni when a chip would have been a much better option due to the goalkeeper being 15 yards from goal.
The visitors’ reward for such enterprising play came six minutes after the restart, when Aluko picked out Brady and he fired across goal for N’Doye to tap in.
Hull should have doubled their advantage four minutes later when Huddleston played in N’Doye but the striker fired across goal and wide of the post.
Jake Livermore then also shot narrowly wide before Yannick Bolasie made a lightning break only for James Chester to clear in front of Yaya Sanogo.
Palace did get the ball in the net with eight minutes remaining but Sanogo was rightly penalised for a tug on Paul McShane’s shirt.
There was still time for Liam Rosenior to volley against the crossbar before N’Doye sealed matters in stoppage time.