Simon Charlton's first goal for eight years helped City secure a point after Pompey had led through goals from Yakubu Ayegbeni and Patrik Berger.
The visitors kicked off attacking the River End goal and won a corner in the first minute but then it was the Canaries who went on the offensive.
David Bentley's corner was cleared before Adam Drury delivered two crosses from the left that failed to find Darren Huckerby or Leon McKenzie.
Berger's seventh minute shot flew inches wide as the ball shaved the top of Robert Green's crossbar.
McKenzie then met Bentley's left-wing cross but his header went inches wide of the near post.
Bentley's in-swinging left-wing corner then hit the near post and rebounded to Charlton whose shot was blocked while at the other end Diomansy Kamara fired over the bar following a quick break by Portsmouth.
Huckerby made a good run down the right wing but when he cut in his pass failed to find McKenzie before Kamara missed the target after a surging run from midfield.
After 36 minutes Green was deceived by Nigel Quashie's swerving long-range shot and when he could only beat it away Yakubu fired in a low right-foot shot to put the visitors one up.
Shaka Hislop made sure he got behind Bentley's low shot as City tried desperately to pull a goal back before half time and Bentley's throughball for Damien Francis forced Hislop to dash off his line to snuff out the danger.
Andy Griffin was the first of three visiting players to be booked for tripping Bentley in first-half stoppage time.
Three minutes into the second half Marc Edworthy saved City with a last-ditch tackle that denied Yakubu when he got on the end of Berger's clever chipped pass.
At the other end McKenzie just failed to get his foot to Huckerby's cross before Norwich briefly got back on level terms.
Bentley was bundled over inside the area and Huckerby stepped up to take the resulting penalty.
Hislop got down quickly to push away the spot-kick, but Huckerby was not to be denied and pounced on the rebound before tucking it under the keeper's body with a low right-foot shot.
Almost immediately Berger restored Pompey's lead with a rasping 25-yard left-foot shot from David Unsworth's short free-kick which curled inside Green's right-hand post.
However, the Canaries were soon back on level terms again when Charlton headed in Drury's cross after good work from Huckerby on the by-line.
Gary Holt then went close to giving Norwich the lead when his fierce shot crashed against the bar and the same player fried inches wide a few minutes later.
Substitute Lomana LuaLua brought a good save from Green and at the other end Norwich substitute Paul McVeigh fired into the side-netting.
In the closing stages Portsmouth's players seemed the happier with the point as they ran the clock down.
MAN OF THE MATCH: Darren Huckerby (Norwich) - His pace caused the Pompey defence problems throughout the 90 minutes and he kept his nerve to net the rebound after his penalty had been saved.