Pompey climbed above Bolton in the League One standings following a narrow victory on the south coast.
John Marquis netted the only goal of the game for Danny Cowley's side early in the second half, with a neat flick to convert Ronan Curtis' delivery.
The visitors had struck the woodwork twice before the break, with former Blues loanee also Eoin Doyle nodding against the crossbar late on, but the battling Blues looked relatively comfortable in the closing stages.
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