Grabban, 25, scored either side of a Yann Kermorgant acrobatic volley to fire the Cherries to their first win in the second tier of English football since Harry Redknapp's side of 1990.
With last season's star-striker Brett Pitman still nursing a knock, ex-Millwall forward Grabban partnered Wes Thomas in attack and opened the scoring with a header on 26 minutes before rifling in the winner from 25 yards on the 66th minute.
Promotion winning boss Howe said: "I am really pleased for him. Every strikerneeds to score and he took his goals really well.
Kermorgant's scissor-kicked equaliser straight after half-time got Chris Powell's side back in the game for the first time but any hope of picking up a point were dashed when Bradley Pritchard saw red for a two-footed lunge on Ryan Fraser after 84 minutes.
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