The former Chelsea striker forced home the winner in the 95th minute of a pulsating cup tie after Uxbridge keeper Sean Dawson had failed to hold Trevor How's stinging shot from the edge of the penalty-area.
Although the Rebels deserved victory for a bustling display, it was rough justice on a Uxbridge side who once again belied their lowly status in Vauxhall League Division One.
The home side made things just as difficult for Slough as they did in the first match at Wexham Park Stadium and will consider themselves unlucky not to escaped from this replay with at least another draw.
The main talking-point of a passionate match was the sensational double sending-off of Uxbridge's Leroy Messitt and the Rebels' Tony Knight after a 34th minute flashpoint. Former Slough midfielder Messitt appeared to continue a running feud with Knight by leaving him sprawled on the ground with a late tackle which necessitated nearly five minutes of medical attention.
But an eagle-eyed linesman noticed that Knight had extracted his revenge by elbowing Messitt in the mouth. And the referee didn't hesitate in giving Knight his marching orders as well.
However, this incident was out of context with an excellent match that enthralled a packed crowd. The Rebels had gone close to snatching the lead before Langley scored their opening goal in the 32nd minute, finishing off a well-constructed move by glancing Neal Stanley's cross beyond Dawson.
Despite a constant bombardment of the Uxbridge goal, Slough were unable to increase their lead and it was a shock when they allowed the home side back into the match in the 64th minute.
Winston White's free-kick skidded off Tony Witter's head and Carl Lindo rose above the Rebels defence to nod home the equaliser.
Slough had their chances to seal victory before the end of the 90 minutes, but it was Uxbridge who spurned the best chance when Ronnie Nelson had a shot cleared off the line by Mark Hill after he had outstripped the Rebels defence.
Slough should have added a third goal in the 112th minute when they were awarded a penalty after Troy Birch handled Steve Thompson's goalbound shot on the line. But Mark Adams — replacing the injured Robbie Johnson as penalty-taker — hit his spot-kick straight at Dawson.
Uxbridge Line up
Dawson, La Croix, McAuliffe, Witter, Proctor, Birch, Messitt, W. White, Nelson, Undo, Pope. Subs: Choules (for Proctor), P. White (for McAuliffe).