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.
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A group of divers have commemorated one century since the end of World War One by hanging a plaque on the bow of a shipwreck off Shoreham.