He beat his marker and cracked a left-foot shot against the bar with home goalkeeper Andy Warrington beaten.
A minute later, at the other end, Rotherham carved out a chance when Ryan Taylor won the ball well but delayed his pass to the unmarked Drewe Broughton and the chance was gone.
But Rotherham were second best as County continued to press forward and, after 14 minutes, Jonathan Forte had Warrington at full stretch to turn his drive away for a corner.
Four minutes later Weston had Warrington furiously back-peddling as he tipped a long-range effort over the bar for a corner.
Rotherham had another let-off after 34 minutes when Matt Hamshaw's shot following a neatly-worked short corner was headed off the line by Nick Fenton.
But a minute later Rotherham suddenly sprang into action when Broughton climbed to meet Taylor's cross but his header was just wide of the upright.
Following Rotherham's first corner in the 39th minute, Ian Sharps had the ball in the net but only after a foul on his marker.
Against the run of play, Rotherham took the lead a minute before the break. Micky Cummins threaded a delightful throughball to Mark Hudson and he raced forward before blasting his shot past Kevin Pilkington.
Rotherham could have had a second in stoppage time, but Jamie Clapham got in a terrific block to deny Rotherham's leading marksman, Reid.
Rotherham hung on to their slender lead until the 69th minute. County continued to play some neat football without producing any real chances and it was Reid who doubled Rotherham's advantage.
Pablo Mills picked out another inch-perfect pass and Reid chased through for his tenth goal in as many games.
But just when Rotherham thought they had made things comfortable, Forte pulled one back.
He chased a long, hopeful ball upfield, brushed his marker Nick Fenton aside and fired past Warrington, but for County it was too little too late.