After seeing title rivals Scunthorpe United held to a draw on Saturday, Chesterfield were unable to take full advantage on a frustrating night at the Proact Stadium.
Their advantage at the summit now stands at two points, while Portsmouth are a step closer to safety having climbed seven points clear of the relegation zone.
The visitors started much the brighter, with Ricky Holmes having a shot saved by Tommy Lee and Jake Jervis hitting the post.
Chesterfield gradually came into the game, but neither Jimmy Ryan or Gary Roberts could beat Trevor Carson with their side's best chances of the half.
With the words of manager Paul Cook no doubt ringing in their ears, Chesterfield began the second period brightly but again lacked accuracy when it came to applying a finish.
Roberts wasted another good chance as he dragged a low shot wide and top-scorer Eoin Doyle saw a header saved by Carson.
Portsmouth were able to hold out for a welcome point that sees them climb four places in the table.
