After a goalless first half at the Magpies' Little Benton Academy, Wooster netted the winning goal in the closing stages, volleying home from Ezra Tika-Lemba's cross.
The Toon teenagers then held firm in the final minutes to record a deserved clean sheet to move within one point of third-placed Everton in the table, with a game in hand over their Toffees counterparts.
Three changes were made from last weekend's 3-2 defeat against Blackburn Rovers, with Jack Callaghan and Luke Gilligan making their first league starts at under-18 level.
With former Magpies goalkeeper Tim Krul in attendance, Newcastle almost got off to a perfect start in the Tyne-Wear derby.
After Wooster pounced upon Finley Robertson's hesitant clearance from goal, the ball landed into Matheos Ferreira's path but the Ashington-born winger's effort at goal was blocked by the left leg of the Black Cats goalkeeper.
Roman Dowell, a representative of England at under-17 level, made a key stop to prevent Sunderland from opening the scoring as the Hebburn-born goalkeeper held Triziano Wilson's fierce volley inside the box.
Wooster went close to scoring in his fourth consecutive league game at under-18 level as Jude Cogdon intercepted the ball on the edge of the box before the ball made its way into the Romford-born striker's path but his low first-time effort was held by Robertson.
The 18-year-old forward, who made his Under-21s debut during August's Premier League 2 visit of Chelsea, missed another opportunity in front of goal after racing onto Cogdon's quickly-taken free-kick but, despite racing clear on goal, saw his placed effort saved by Robertson.
Newcastle's youngsters were fortunate to remain on level terms before the half-time whistle as a teasing corner dropped into Arron Bowman's path but the Sunderland full-back lifted the ball over the crossbar.
In the second half, Newcastle withstood a further attack as James Barker's bending strike flew beyond the left-hand post.
United continued their pursuit for a breakthrough as Gilligan's teasing delivery from the left flank was turned out for a corner by Matthew Burns.
In the 77th minute, Newcastle took the lead through Wooster's impressive finish. After Tika-Lemba regained possession in a dangerous position, the right-back's lofted cross found Wooster inside the penalty area before the in-form striker fired his downward volley into the right-hand corner.
With the full-time whistle nearing, Dowell produced a crucial double save to ensure maximum points as the 16-year-old shot-stopper parried Barker's free-kick on the edge of the box before reacting quickly to hold Bowman's rebound.
Newcastle United Under-18s: Roman Dowell, Ezra Tika-Lemba, Guy Bloomer, Isaac Moran (Aaron Epia 46), Henry Johnson (c), Jude Cogdon, Sammy Pinnington, Jack Callaghan (Alfie Hutchison 83), Kacey Wooster (Ethan Ndiweni 90), Luke Gilligan (Noah Morgan 69), Matheos Ferreira.
Subs not used: Oliver Holland.
Photograph courtesy of Finlay Henderson
