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 substitute Callum McManaman was sent off just three minutes after coming on.
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 bar by Ryan Allsop.
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