Argyle were ahead after just a couple of minutes as home defenders Andy Melville and Chris Doig got in a tangle and loanee Blackstock drove his shot past the stranded Paul Gerrard.
Hasney Aljofree and Norris went close with efforts from distance as Forest reeled from the early setback and the latter doubled the visitors' lead midway through the first half.
Norris was allowed time and space to try his luck and his shot deflected off Wes Morgan to again leave Gerrard with no chance.
Gareth Taylor headed a Kris Commons against the crossbar just before the interval and Aljofree did likewise just after the restart from an Akos Buzsaky corner.
Blackstock nearly got his second of the game just before the hour, but was denied by Mathieu Louis-Jean's covering challenge, but the Southampton youngster made no mistake soon after.
Norris did the spadework and set up his team-mate for an easy close-range finish.
Nick Chadwick almost added a late fourth to heap more misery on a woeful Forest side.