The Reds remain 12 points off the play-off places but showed that their revival under the new stewardship of Dougie Freedman is a genuine one.
Prior to Wednesday night, Forest's four games with the Scot in charge had been against teams battling against relegation but against high-flying Bournemouth they battled back from the loss of an early goal to claim all three points.
Surman gave the visitors the lead on 3 minutes before Lascelles (21) and Lansbury (44) ensured the hosts of a half-time lead.
That was maintained and the Reds also had their chances to increase it despite the Cherries dominating possession.
20,637 watched the action and Forest now travel to face Reading on Saturday afternoon.
Read a full Match Report here.