Despite taking the lead in the 14th minute when Kevin Ellison struck with a low left-footed shot from the edge of the box, Chester were hit by a goal barrage from the visitors in Tuesday night’s League Two clash at the Deva Stadium.
Reid hit the crossbar early on, but then drew his side level in the 26th minute when Kevin Roberts handled in the box, and the striker made no mistake from the spot.
The Millers went ahead after 38 minutes when a Jamie Green cross from the left was met by a header from close range by Micky Cummins.
And in first-half added time Reid’s cross deflected off Roberts and was headed home by Drewe Broughton.
A fourth was added five minutes into the second half when Reid hit a rising left-footed strike and he completed his hat-trick after 72 minutes with a superb right-footed shot as Chester completely folded.