Pitman, on his second debut for the Cherries after sealing a loan move from Bristol City in midweek, robbed Ethan Ebanks-Landell before curling home a shot from 18 yards in Saturday's League One clash at Gigg Lane.
Bury went in front in the 15th minute when Matt Doherty crossed from the right and loan striker Troy Hewitt swept the ball home from six yards for his second goal in two games.
Bury's Peter Sweeney curled in a free-kick which veteran ex-England goalkeeper David James saved brilliantly, while the Cherries hit back with former Bury midfielder Marc Pugh seeing a shot blocked.
Doherty's header was then blocked by a combination of the post and Bournemouth's Charlie Daniels, who created Bournemouth's equaliser just before the hour-mark as his cross was slotted home by Lewis Grabban from six yards.
Bury went back in front with 12 minutes left as David Worrall pounced to beat James after his initial shot had rebounded back to him off Miles Addison, but Pitman kept Howe's unbeaten run intact.