While at Ipswich last season, Norris scored home and away against Burnley, and he proved to be a thorn in the Clarets' side once more.
The 30-year-old attacking midfielder missed a good opportunity to claim the points from Greg Halford's cross in the 78th minute, but he made amends 45 seconds into time added on by smashing a left-footed shot into the bottom corner from 20 yards to settle a scrappy contest.
Despite heading into the game looking for a fourth consecutive win, Burnley were strangely subdued in a first half where the visitors were the better side.
Luke Varney failed to convert a close-range opportunity in the third minute, before a collision with Clarets goalkeeper Lee Grant resulted in a rejected penalty appeal and an early end to the forward's afternoon through injury.
Eddie Howe's home side performed with greater authority after the interval and skipper Chris McCann passed up their two best opportunities, while a pair of rasping long-range efforts from Ross Wallace were narrowly off target.
Portsmouth almost took an early lead when Grant parried Norris's shot into the path of Varney, but the former Charlton man was unable to make a clean contact and Kieran Tripper hacked clear.
Varney escaped the attentions of Burnley's defence after a quarter of an hour and lobbed goalwards before colliding with Grant, but as the Pompey attacker lay prone on the floor, referee Steve Rushton signalled for a home free kick.
Two periods of treatment followed and Varney eventually made way for Erik Huseklepp - the man he replaced in Michael Appleton's starting line-up - after 20 minutes.
Burnley looked nothing like a side on a run of three straight wins as they struggled to retain possession and Grant gathered at the second attempt following a drive from Hayden Mullins.
Portsmouth striker Dave Kitson got his head to a Norris' free kick three minutes from the end of a disappointing, disjointed first half, but his effort looped over.
Ross Wallace drilled a 47th minute free-kick wide as Burnley enjoyed their first attempt on goal, before Clarets strike duo Sam Vokes and Jay Rodriguez combined well to engineer a chance for midfielder McCann and Pompey keeper Stephen Henderson tipped over.
The visitors responded with a sweeping move after 56 minutes, which resulted in Huseklepp angling a volley past the post from inside the area.
Shortly before the hour Burnley forward Martin Paterson came off the bench for his first action since suffering a thigh injury in the opening game of the season.
The 24-year-old's first contribution was to lay off Vokes' knockdown to Wallace, and the Scotland winger aimed a stinging 30-yard half volley narrowly past the upright.
McCann headed wide in the 67th minute as a quickly-taken corner caught Henderson napping, but Portsmouth soon made their presence felt at the other end when Huseklepp drilled across the six yard box and David Edgar scrambled to safety.
Norris prodded Halford's cross wide with 12 minutes to play, although he redeemed himself in style at the death.