Norway remain in third spot in Group H on 13 points but are now only a point behind second-placed Croatia after seven matches. Italy, who beat Malta 1-0, top the standings on 15.
Victory was secured at the Vasil Levski stadium when Forren escaped his marker Georgi Milanov down the right and gave keeper Bozhidar Mitrev no chance with a precise shot from close range after Stefan Johansen's clever free kick into the area.
Alexander Soderlund almost doubled Norway’s lead a few minutes later when he headed just wide from a left-wing cross.
Bulgaria struggled to create any clear-cut chances against well-organised defence with captain Ivelin Popov coming closest to scoring midway through the first half when his curling free kick forced an excellent save from Orjan Nyland.
Bulgaria, who were booed off the pitch, are fourth in the group with eight points and have only a remote chance of making the top three.
On Sunday, Norway host Croatia while Bulgaria visit Italy.
(Reporting by Angel Krasimirov; Editing by Ken Ferris)
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