Elyounoussi latched on to Per Ciljan Skjelbred's lofted pass before dodging round keeper Nikolay Mihaylov and then lifted the ball over Apostol Popov to score in the 13th minute.
Bulgaria stuck back before the break when Nikolay Bodurov powered a header into the net from a corner.
Having lost striker Joshua King to injury on the hour mark, the Oslo crowd got a welcome lift shortly afterwards when coach Per Mathias Hogmo brought on 15-year-old Martin Odegaard, Norway's youngest-ever international, for his second cap.
The teenage playmaker immediately provided a much needed spark of creativity for Norway.
Captain Skjelbred made a surging run through the Bulgarian defence before flicking the ball onto the path of Nielsen, who hooked his shot home.
Norway are third in Group H with six points from three games. Leaders Croatia, who thumped Azerbaijan 6-0, and second-placed Italy are both on nine points.
(Reporting By Philip O'Connor in Copenhagen, editing by Pritha Sarkar)
Share
