Bournemouth eased into the second round of the FA Cup and a home tie with Carlisle United but only after veteran former Nottingham Forest defender Des Lyttle had given them a late scare.
With only Forest Green's second shot on target with two minutes remaining Lyttle stepped forward to score with a blistering 25-yard drive into the roof of the net.
By then Bournemouth were holding a two-goal lead and there were some nerves until substitute Dani Rodrigues finished off the resistance.
Forest Green played with only one striker, Charlie Griffin, in attack and frustrated Bournemouth for ten minutes until Alan Connell opened the scoring.
Gareth O'Connor sent a cross in from the left and Connell swept in a headed pass from Derek Holmes.
O'Connor shot across the face of the goal and Dean Williams raced outside his area to prevent Holmes getting through but a second goal was inevitable.
It came an hour after the first and again O'Connor was involved, his deft pass setting up an easy shooting chance for John Spicer to score his fourth goal during his loan spell from Arsenal.
Williams made a great save on his line to deny substitute Shaun Maher before Lyttle raised the spirits of Forest Green's small band of travelling fans by scoring his spectacular goal.
Forest Green began to entertain thoughts of extra-time but then, committed to attack, they left a big gap at the back that O'Connor exploited with a pass for Rodrigues to run on and beat the unprotected Williams.
Williams had earlier proved to be Forest Green's saviour with a save at the second attempt to keep out Spicer while manager Alan Lewer sent on Jefferson Louis, scorer of the goal which earned the replay, in the 59th minute in a bid to liven up his attack.
Louis posed problems in the air but had little chance to shine against a defence that was well-marshalled by Eddie Howe.