The draw follows back-to-back wins for Forest, who are now just one point behind Wolves in the Championship.
Despite being on the back foot in the opening exchanges, Wolves took the lead in the 15th minute when Ethan Ebanks-Landell found the space to head home from Jordan Graham's corner.
Wolves felt they should have been awarded a penalty when Adam Le Fondre appeared to be brought down by Mills, but the referee ignored the protests from the home players and supporters.
More chances arrived for the hosts before the break as Dorus de Vries kept out a deflected effort from Le Fondre, before Graham found the side-netting with a shot after linking up with James Henry in the box.
Ebanks-Landell threatened to score his second of the night when he connected with a corner, but a miscued header was eventually cleared from the box.
Forest soon came back into the game and a patient passing move created an opening for Ben Osborn, who hesitated to ensure that his effort was blocked.
Wolves could have killed the game off late on when Ebanks-Landell once again met a corner to head wide as Forest struggled to put the pressure back on Kenny Jackett's side.
However, Blackstock made the vital contribution with 10 minutes remaining by volleying home from a corner to deny Wolves victory and move Forest up to 15th in the table.