Midfielders Danny Harrison and Mark Hudson also came close to claiming the distinction of the side's first league goal at their new temporary home Don Valley Stadium.
Ryan Taylor crowned an eye-catching first-half performance with a header that might have caught out keeper Rob Burch but it fell wide.
Mark Lynch whipped in a low cross from the right and Reid reacted sharply to go close with a crisp first-time shot
Referee Andy Haines was the target for home fans when Lincoln 'keeper Burch raced from his area to cut out a long ball and appeared to palm the ball down five yards out of his area only for the official and his assistant to dismiss Rotherham's claims.
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But a minute before the break, Rotherham took a deserved lead when Reid showed his pace and strength to out-muscle Lee Beevers and rifle a cool shot past Burch after Mills set him up with a long ball forward.
Seconds before the break, Taylor almost added a second when he went round Janos Kovacs but was shut out when Beevers and Burch combined to block him.
And two minutes into the second half, Harrison did well to fire a testing shot that had Burch stretching and, when Reid found the target with a long-range effort, Burch made a comfortable stop.
Lincoln were denied an equaliser after 66 minutes when Stefan Oakes produced a dipping free-kick from 30 yards, but Warrington stretched to tip it over the top and the Millers held out despite some late pressure to secure their win.