Former England midfielder Anderton executed a textbook left-foot volley from just outside the penalty area on 19 minutes after Millwall goalkeeper Lenny Pidgeley had punched away a Steve Fletcher header.
Bournemouth, fresh from the news of a takeover by local businessman Jeff Mostyn and Steve Sly, started the brighter of two sides - who have very different agendas this season.
The Cherries, fighting for survival at the foot of League One, almost took the lead on five minutes when James Hayter's turn and volley flew just wide of Pidgeley's left-hand post.
Willie Donachie's Millwall on the other hand still harbour desires of a late run towards the top six and were the form side going into this game having won six of their last eight.
None of that was evident though as Marc Wilson's long throw was flicked on by Fletcher and, despite Pidgeley getting a clean fist on the ball, he only happened to direct it as far as Anderton who wasted no time in lashing it home in trademark fashion.
The Lions struggled to claw their way back into the game and looked a tired and weary side after their gruelling 2-2 draw with Crewe earlier in the week.
David McGoldrick should have doubled the lead ten minutes after the break when he was put through by Josh Walker.
Veteran defender Richard Shaw managed to push the teenage striker away from goal, but McGoldrick still managed to get a decent strike away only for Pidgeley to save well with his left hand.
Hayter then went close with two more chances as Bournemouth failed to match their possession with goals and there was always a slight danger of the in form Millwall striking back.
Indeed, on 72 minutes, Bournemouth's second biggest league crowd of the season had their hearts in their mouths when Marvin Elliott's miscued shot deflected off Darren Byfield's thigh to loop high over Neil Moss but landed just inches wide of the far post.