Pitman's 12th goal of the season settled a scrappy game which saw Oldham, who remain in the League One drop zone, squander a second-half penalty.
The crucial strike came after 22 minutes when a sharp move down the left ended with Lewis Grabban crossing to Pitman for a six-yard finish.
Pitman forced an alert save from Oldham keeper Dean Bouzanis, while Grabban also went close to doubling the visitors' lead.
Oldham's first real effort came on the hour as Jordan Obita's angled shot was tipped round the post by Ryan Allsop.
But the Latics wasted a golden chance after 70 minutes when they won a penalty for Grabban's handball - Jose Baxter dinked his spot-kick down the middle and Allsop clawed it out despite diving to his right.
Baxter almost made amends, but Allsop beat away his 25-yard free-kick to earn Bournemouth back-to-back victories.