Pompey conceded a late penalty to ensure their frustrating start to the season continued at Adams Park.
Adebayo Akinfenwa netted the only goal of a largely dour contest from the spot after Tom Naylor had been penalised for handling in the box.
Both sides were reduced to 10 men, with Nnamdi Ofoborh shown a straight red card and Ellis Harrison dismissed for two bookable offences.