Paul Lunan bagged a double inside half an hour and a late wonder strike from David McClune sealed all three points.
Lunan opened Forfar's account after only five minutes when he met a Darren Gribben corner and tucked it home at the far post.
He doubled his tally in the 24th minute when he was again left unmarked at the rear post to pounce on the ball after it broke from Gribben.
Alloa only really started to play after they were two goals down but they had by far the better chances for the remainder of the match.
Chris Townsley blazed a shot just over the bar before the interval and after the break Paul McLeod should have done better than to shoot weakly into Sean Murdoch's arms.
Lunan saved his side when he cleared a goalbound Ross Hamilton shot off the line. Then Murdoch tipped a shot from Hamilton over the crossbar.
Forfar rode out the pressure however and with nine minutes left McClune made sure of the points with a stunning 25-yard shot which curled into the top corner.