Pompey were unable to salvage a point against Doncaster, despite a late fightback.
The 2-1 defeat at the Keepmoat Stadium saw Kenny Jackett's side drop one place to fifth in the League One standings.
Reece James and Fejiri Okenabirhie gave the hosts a commanding lead, with John Marquis reducing the deficit in stoppage-time and the Blues almost snatched an equaliser with the final kick.
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