Rookie midfielder N'Diaye, 19, struck after 63 minutes as Palace pulled off a perfect smash and grab raid at The Hawthorns.
Palace frustrated Albion for long spells while Luke Moore wasted two fantastic chances to put Roberto Di Matteo's side in control before N'Diaye pounced.
The defeat also cost Albion the chance of equalling a club record of starting the season with a nine-match unbeaten run in the league - something they had only done twice before in 1953 and 1999.
But for Palace it was another sign they are turning the corner after an inconsistent start to the season.
They have now won their last two games and have back-to-back home games against Sheffield Wednesday and Blackpool to look forward to as they seek to continue their revival.
Albion set the tone for themselves when they were let down by their finishing in a low key opening period with Shelton Martis and Moore both squandering excellent opportunities from close range.
Martis saw his 12th minute shot deflected over the bar before Moore blazed over his effort from an almost identical spot after good work by Gonzalo Jara and Gianni Zuiverloon.
Goalkeeper Julian Speroni then denied Jara before Palace showed they more than carried a threat of their own on the break through the lively Victor Moses.
Twice he used his pace to power clear but, like his Albion counterparts, his finishing let him down as he blazed his shots wide.
Albion continued to squander chances in the second half with Moore again the chief culprit.
After another cross from Zuiverloon in the 58th minute, Moore only had Speroni to beat but the former Dundee keeper spread himself and blocked the shot.
It was a costly miss as Albion were undone just five minutes later when Danny Butterfield swept a long free-kick into the Albion area.
Alan Lee, who had only been on the pitch for two minutes, rose above the Albion defence and flicked on the ball into the path of N'Diaye, who bustled his way to the near post before bundling his shot past Scott Carson.