Pitman struck five minutes from the end with a spectacular dipping 25-yard volley into the top right-hand corner.
But it was a victory the Cherries scarcely deserved in a match generally devoid of goalscoring chances.
Bournemouth were so ravaged by injuries that they were only able to name three substitutes, one of whom was 15-year-old schoolboy Jayden Stockley.
Their patched up side played second best to Burton until well into the second half, when the introduction of substitute Alan Connell fired the home side.
On-loan Polish goalkeeper Artur Krysiak made a brilliant one-handed save to deny veteran Bournemouth striker Steve Fletcher, while at the other end substitute Greg Pearson wasted Burton's best two chances.