Lewis Grabban was denied by U's goalkeeper Sam Walker after 17 minutes after bursting onto Eunan O'Kane's pass.
But the Cherries did take the lead two minutes later when Pitman fired in a first-time shot at the near post from Matt Ritchie's low cross to leave Walker with no chance.
The visitors were the better side in the first half and Marc Pugh's header at the far post from Harry Arter's cross was deflected onto the post, while Grabban wasted a gilt-edged chance in first-half stoppage-time when he shot wastefully wide after breaking the offside trap.
Bournemouth almost doubled their lead early in the second half when Walker denied Arter after the midfielder had exchanged passes with Pitman before firing in a close-range shot.
Arter fired straight at Walker midway through the second half and then tested the U's keeper again with 11 minutes to go as Bournemouth secured a vital win to move into the automatic promotion places, two points behind league leaders Doncaster.