Pompey had to remain patient in order to see of a stubborn Forest Green side at Fratton Park.
John Mousinho's men were totally dominant in possession before the break, only to be met by resistance from a side who got everyone behind the ball.
But they did break the deadlock early in the second half, when Owen Dale climbed above a defender at the back post to convert Joe Rafferty's cross.
Dale had a couple more great chances to put the result beyond doubt, but the visitors offered little at the other end to threaten the Blues' win.
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