Chesterfield would have gone four points clear at the top of League Two with a home victory but Portsmouth had the better chances and are now seven points clear of the drop zone.
Chesterfield went into the game at the Proact Stadium, as clear favourites but Portsmouth almost scored in the ninth minute when Jake Jervis got in on the left but Tommy Lee touched his shot against a post.
Pompey were playing with confidence although goalkeeper Trevor Carson had an anxious moment in the 26th minute when he failed to hold a 25-yard shot from Ollie Banks but recovered before Eoin Doyle could pounce.
Dan Gardner flashed a low free-kick just wide from the right edge of the box in the 40th minute after a handball by Ben Chorley and Gary Roberts was only just off target when he found space on the Portsmouth left three minutes into the second half.
Jervis gave Chesterfield another scare when he fired narrowly wide in the 59th minute and Wes Fogden was foiled by Lee when he was through in the 66th minute.
Marc Richards had a chance to win it for Chesterfield in added time but headed straight at Carson from eight yards.