Grabban, 25, found the back of the net either side of a stunning Yann Kermorgrant scissor-kick to give the Cherries all three points on their return to the second tier of English football.
Things got worse for Charlton when Bradley Pritchard saw red late on for Chris Powell's side after a two-footed lunge on substitute Ryan Fraser.
It was the London side who started brightly and left winger Callum Harriott fired the game's first chance over the bar after six minutes.
But Bournemouth responded well and after new French recruit Mohamed Coulibaly had curled a right-footed effort wide, they took a deserving lead after 26 minutes.
Good work down the right from Steve Cook forced a corner which Marc Pugh took quickly to Harry Arter.
The former Charlton academy prospect curled in a left-foot cross which Lewis Grabban rose highest to meet and guide past a stranded Ben Hamer.
Former Charlton star Scott Parker would have been proud of his brother-in-law Arter, who was the driving force in Bournemouth's midfield.
The promoted side were flying and Wes Thomas was inches away from doubling the lead minutes later but his sliding effort from a Pugh cross whistled just wide.
Grabban then went on a duel with his nemesis Hamer but came off second best with the goalkeeper denying the forward's next three attempts.
Charlton were looking to carry on from where they left off last season where a good run of form saw them finish just three points outside the play-off places.
As they pushed for an equaliser their new loan signing, former Olympic striker Marvin Sordell, exchanged passes with Harriott, who dragged a left-foot drive wide of Ryan Allsop's post.
Straight after the break they were back on level terms. Shaun MacDonald deflected a Harriott cross into the path of Kermorgrant, who acrobatically rifled a scissor kick past a stunned Allsop.
But they were not level for long. Grabban, who scored 13 goals last season, picked up the ball after 66 minutes and drove right-footed past an outstretched Hamer to send the home fans wild.
Wales international Simon Church, who only signed for The Valley club in the week, was introduced soon after but failed to inspire an equaliser.
The closest they came to grabbing a point was when Pritchard had a header cleared off the line by Cherries new boy Elliott Ward after 80 minutes.
Moments later the result was all but sealed when Pritchard took an early bath for his frustrated lunge on Fraser.