Pompey, who had goalkeeper Aaron Flahavan to thank for a series of great saves, stay in the bottom three on goals scored, while John Aldridge's side failed to improve on their 16th position.
"The way we performed on a wet night was terrific," Alan Ball, the Portsmouth manager, said. "We have five games left and I am proud of the way the players are setting about staying in this division."
In the Second Division Kevin Keegan's Fulham missed a chance to cement their position in the top six, when they dropped two home points against Walsall in a 1-1 draw. They needed a goal from substitute Paul Trollope three minutes from time to cancel out the opener from the Frenchman Roger Boli.
Burnley's relegation plight worsened when they lost 2-1 at home to Blackpool and had on-loan striker John Mullin sent off six minutes from time.Reuse content