The result brings to an end a run of five consecutive defeats for the Cherries, who remain outside the play-offs but are just four points behind second-placed Sheffield United.
Lewis Grabban came close in the 17th minute when he controlled Pitman's long ball before his stabbed effort was kept out by Stevenage goalkeeper Steve Arnold.
The Cherries broke the deadlock in the 38th minute when Arnold took out Eunan O'Kane after the midfielder's shot and up stepped Pitman to calmly roll in the resulting penalty.
Boro began the second half brightly and Steve Cook had to be in the right place at the right time to clear away Lucas Akins' flicked header from Luke Freeman's free-kick.
Things went from bad to worse for the hosts in the 90th minute when they had Darius Charles sent off for a dangerous tackle on Harry Arter, who was stretchered off as a result.