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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Oxford's most famous hotel, the Randolph, is ablaze after a fire started in the roof space. 12 fire crews are on location in the city.
Friday night's weather for the east of the region
Friday night's weather for the west of the region