The Scholars broke the deadlock in the 28th minute. Reid's corner was powered home by James Askey.
Castle had their first shot on target at the start of the second period. James Steele scuffed his effort and Curtis Pond easily gathered the ball.
Reid earned his second assist with a chipped free kick that was bulleted home by skipper Ryan Wynter in the 51st minute.
Askey was inches away from his second with a header from a George Cater corner.
Newcastle were reduced to ten men when skipper Sam Bradbury received a second yellow card for a late lunge on Danny Cocks.
The Scholars extended their lead from the penalty spot after Taylor Attrell bundled Cater to the ground. Jack Langston made no mistake powering the ball past Matthew Johnson.
Langston added his second penalty after Danny Cocks was felled by keeper Johnson and the Chase number 8 fired into the opposite corner.
Chasetown deservedly made it 5-0 when Jazz Luckie's cross fell to the feet of Cocks who picked his spot and drilled it past Johnson.