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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The latest weather for the east with Philippa
The latest weather for the west with Philippa
Met Office issues storm warnings overnight as 80mph winds are expected across the south and east. Storm Imogen is due at around 3am