The Crystal Palace youngster held his nerve just after the hour to score the only goal of the game and secure a deserved victory for Neil Warnock's men against the league leaders.
Luke Moore and Graham Dorrans came closest to netting for Albion, who were brought back down to earth with a bump following their 5-0 thrashing of Middlesbrough last weekend.
The visitors were clearly not daunted by the prospect of coming up against the high-flying Baggies as Neil Danns crashed a 25-yard effort just over with barely two minutes gone.
Danns went close again from a similar distance five minutes later and had a header from a Danny Butterfield cross saved by Scott Carson as Palace enjoyed a lively opening.
It took over 20 minutes for West Brom carve out their first noteworthy opportunity of the afternoon, Gonzalo Jara firing straight at Julian Speroni from the edge of the penalty area.
The lively Victor Moses - who has yet to open his account for the season - twice tried his luck from long distance, but on both occasions failed to force Carson to make a save.
Speroni had to be alert after 39 minutes to ensure Dorrans' inswinging corner did not find a way past him, while Darren Ambrose shot wide from 20 yards at the other end on the stroke of half-time.
Palace continued to press straight from the restart, Danns drilling wide right-footed from fully 30 yards, with Dorrans also going close for Albion inside the opening exchanges of the second period.
Just before the hour mark, Speroni produced a fantastic save to keep out Moore's close-range effort after the former Aston Villa trainee had raced on to Gianni Zuiverloon's cross.
Zuiverloon and Moore were then hauled off and replaced by Reuben Reid and Simon Cox respectively as Albion boss Roberto Di Matteo attempted to add some attacking bite into his side.
However, it was Palace who deservedly broke the deadlock after 63 minutes.
Shelton Martis should have dealt with a punted long ball but hesitated and N'Diaye pounced to coolly sidefoot past Carson for his first senior career goal.
Jonas Olsson could - and perhaps should - have levelled for Albion four minutes later when he met another threatening Dorrans corner, only to see his near-post header flash over.
Roman Bednar headed wide from six yards and Dorrans shot over from 18 yards as Albion continued to create and spurn chances.
Joe Mattock was denied by Speroni from 20 yards as Palace found themselves camped in their own half late on, but held on for the three points.