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Rotherham looked sharp at the start when stand-in Wolves keeper Carl Ikeme reacted quickly when quick-fire striker Reid threatened to give the League Two side a lead inside the first minute.
Reid, scorer of an equalising goal and penalty in the shoot-out win over Sheffield Wednesday in the previous round, tore forward but Ikeme threw his body in and blocked.
And when Mark Hudson flighted a testing ball forward, Alex Rhodes raced in behind the Wolves defence but Ikeme did well.
The Championship side's first opportunity came when Michael Kightly aimed an accurate corner, but Neil Collins was off target with a free header.
Stephen Ward had the ball in the net for Wolves but was clearly offside and, when a poor header from Harrison fell for Ward on 24 minutes, he fired over.
Five minutes later, Wolves saw another opportunity wasted when Dave Edwards fired a 25-yard free-kick over.
Eight minutes before half-time, Rotherham were denied when Harrison smashed a 25-yarder and Ikeme appeared to tip it over the top.
And when Kightly went sprinting forward on the break, Harrison made a crucial intervention.
Wolves hung onto possession in the dying minutes of the first half and Ward went close with a curling effort from the edge of the area.
Wolves beefed up their strikeforce in the second half as Andy Keogh bowed out and big frontman Chris Iwelumo came on.
But Rotherham continued to hold their own against the Championship side and new signing Andy Nicholas had the visitors in trouble with a long throw but it skidded off Nick Fenton's head.
In a grim second half, Rotherham went close when Lynch crossed in from the right and Harrison met it but couldn't find the target.
Seconds before the end of normal time, Rotherham's Drew Broughton dragged a shot wide from 10 yards as Wolves were in a panic.
In extra time Rhodes almost squeezed a long range shot under Ikeme, before Ryan Taylor blazed wide and Elliott saw a late shot deflected for Wolves.