Grabban scored in the 43rd minute before the Cherries squandered the chance to go two goals clear when Brett Pitman missed a penalty 10 minutes after half-time.
The Latics' task became harder just minutes later when second-half substitute Callum McManaman was sent off just three minutes after coming on for a lunge on Pitman.
Bournemouth boss Eddie Howe started at right-back the last time the Cherries beat Wigan in the league 12 years ago.
It took Wigan two attempts to beat the Cherries on their way to FA Cup victory last season and James McCarthy came close to opening the scoring after seven minutes when his dipping 25-yard effort was tipped over the crossbar by Ryan Allsop.
Owen Coyle's men, one week on from their defeat to Manchester United in the Community Shield, failed to reproduce the form that saw them crush Barnsley 4-0 on the opening day of the campaign.
Two million pound man Grant Holt was making a nuisance of himself but could not fashion an opening.
Bournemouth were not having such trouble and ex-Millwall striker Grabban went close with a spectacular overhead kick moments before firing in the opener.
Wigan summer signing James Perch under-hit a calamitous back pass and goalkeeper Carson could only watch as the opposing number nine nipped onto the ball and guided it underneath him.
The game exploded into life in the second half and Grabban's strike partner Pitman should have made it two when he was awarded a penalty by referee Graham Scott after being brought down by Stephen Crainey.
But former England stopper Carson guessed correctly down to his right and ensured the Cherries top scorer from last year would not get on the score-sheet on his return to the starting line-up.
Coyle bought on exciting duo McManaman alongside James McClean after 55 minutes but the decision backfired soon after when the former took an early bath, which resulted in ugly scenes from both sets of players and benches.
Wigan were up against it and only went close to equalising when Marc Pugh hacked a Leon Barnett header off the line.
With a one-man advantage, Bournemouth were looking for the second and would have got it but for Carson clawing out a quickly taken Pitman free-kick after 85 minutes.