Steve Bruce's side lifted themselves into 16th in the Premier League table after a valuable victory at Selhurst Park, the Senegalese striker scoring just after half-time
Steve Bruce's side had been winless since overcoming QPR 2-1 in February and faced the prospect of ending Saturday in the bottom three if they came away from Selhurst Park empty-handed.
N'Doye netted the decisive late goal against the Rs and he was Hull's hero once more here when he poked the ball home from close range seven minutes into the second half before sealing the points in stoppage time.
Palace had belatedly rallied prior to that second and substitute Yaya Sanogo saw a header disallowed for fouling Paul McShane.
Hull sub Liam Rosenoir then clattered the crossbar with a long-range volley in the closing moments but it was N'Doye who had the final word when he ran clear on the break and finished clinically to edge his team up to 16th - two places and a solitary point above the relegation zone.
Palace made changes in the full-back positions, with Martin Kelly and Pape Souare coming in for Joel Ward and Joe Ledley, while Alex Bruce made way for midfielder Robbie Brady as Hull opted for a back three.
Tigers defenders Michael Dawson and James Chester got in each other's way trying to clear a seventh-minute free kick and Hull goalkeeper Steve Harper saved brilliantly when Palace striker Glenn Murray looked to dispatch the loose ball.
Hull should have taken the lead in the 14th minute when Brady's magnificent left-wing centre picked out N'Doye but the forward inexplicably steered the ball away from goal despite being unmarked at the back post.
The visitors were enjoying the better of an end-to-end contest by the time that Palace goalkeeper Julian Speroni pushed Tom Huddlestone's curling effort away from the top corner.
Palace crafted the next clear opening in the 27th minute when Jason Puncheon slipped a pass into the area for Wilfried Zaha, who drew a save from Harper after a superb first touch.
Speroni came off his line to parry Jake Livermore's chip as a breathless first half ended goalless.
Hull resumed on the front foot and Speroni turned an N'Doye header from Ahmed Elmohamady's searching cross round his near post.
N'Doye's luck in front of goal finally changed in the 52nd minute when Sone Aluko picked out Brady, who bundled the ball past Speroni to leave his team-mate with a tap-in. The Senegal striker almost doubled his tally three minutes later but dragged a shot wide after Huddlestone had beaten the Palace defence with a deft piece of footwork.
Hull continued to push Palace back inside their own half but Chester made a vital clearance when Yannick Bolasie broke clear.
Sanogo's 83rd-minute celebrations were cut short when he was adjudged to have fouled McShane, as Palace headed towards back-to-back losses for the first time in the Premier League under Alan Pardew.
After Rosenior's spectacular effort against the woodwork, Palace debutant Lee Chung-Yong then gave away possession and N'Doye stormed through confidently to wrap up all three points.