An open and entertaining match played on a freezing night had seen both sides take the initiative only to be pegged back, although Wolves must have thought they had won it when Carl Cort scored in the last minute.
But in the second minute of added time, a free-kick was headed against the Wolves crossbar by Grzegorz Rasiak and Reich put away the rebound.
But both sides will also point to a controversial second-half penalty from Inigo Idiakez which was retaken three times before the Spaniard could celebrate his second goal of the game.
It all added up to pulsating viewing for a 24,000 plus crowd on a bitterly cold night, although both managers will be far from happy with the defending.
Derby always looked vulnerable when the ball was played into the box and Wolves thought they had taken a fourth minute lead when Joleon Lescott headed in only to be ruled offside.
Five minutes later Idiakez curled in a free-kick from 25 yards for his 6sixth of the season, but Wolves pulled one back within three minutes.
Rob Edwards, who was on loan at Derby last season, made a strong run into the Rams penalty area before pulling the ball back for Kenny Miller to head in from point-blank range.
The second-half was just as topsy-turvy, with Derby making two changes and switching to a 4-4-2 formation.
It gave Wolves more space and they should have taken a 55th minute lead when Miller was denied by Lee Camp and Ki-Hyeon Seol blasted the ball over the bar from ten yards.
It was a bad miss and Wolves needed a fine save from Michael Oakes to deny Adam Bolder in the 64th minute.
But Derby were again punished for their frailty in the air when Paul Ince swung in a free-kick from the right and Lescott headed in from six yards.
The home side hit back straight away and when Paul Peschisolido was tripped by Edwards, Idiakez put away the penalty only for it to be retaken for encroachment by a Derby player.
Oakes saved the second spot-kick, but again the referee ordered a retake, and after the keeper was booked, Idiakez put Derby level.
Cort restored the visitors' lead when Miller crossed from the right, but Derby at least got something from the game when Wolves were caught out by that last-gasp free-kick.