The African side fell behind in the international friendly but battled back, with the Super Eagles, who are set to compete in this summer's World Cup, grabbing a late draw
In the first of three friendlies in the build-up to Brazil, Stephen Keshi left the likes of Vincent Enyeama and John Obi Mikel out of the matchday squad against a Scotland side resurgent under Gordon Strachan.
Scotland are now six games unbeaten but were denied a fifth win in that run by Nwofor's late equaliser at Craven Cottage.
Charlie Mulgrew gave them the lead 10 minutes in when he produced a clever flick to divert James Morrison's long-distance effort over Nigeria's second-choice goalkeeper Austin Ejide.
However, Nigeria were level four minutes before the break when Michael Uchebo's effort from outside of the area was deflected in off Grant Hanley.
Gordon Strachan's side were back in front early in the second thanks to Azubuike Egwuekwe's own-goal but Nwofor pounced on sloppy defending from Gordon Greer and Hanley to fire home.
It leaves Keshi with much to ponder ahead of friendlies against Greece and the USA and their Group F opener against Iran in Curitiba on June 16
Ikechi Anya went close early on, as he chested a long ball down and shot across goal only for his effort to strike the post before Uchebo's effort at the other end was saved - as he intercepted a careless pass from Alan Hutton.
Mulgrew then produced a moment of magic as he managed to flick Morrison's wayward effort over Ejide.
Shola Ameobi should have come closer to equalising but could only spoon a free-kick over with Shaun Maloney next to hit an effort high and wide from distance.
Scotland almost edged two goals ahead when Hanley headed a ball in - only for the Blackburn Rovers defender to be denied by the referee's whistle after he was adjudged to have fouled Ejide.
Hanley's misfortune continued before the interval as he was the unlucky party to deflect Uchebo's strike past Allan McGregor.
However, Scotland restored their lead after the break when Egwuekwe inadvertently turned the ball into his own net following Hutton's cross.
Maloney thought he had extended their advantage when he tapped home Hutton's delivery before the linesman flagged for offside.
Keshi introduced attacking trio Victor Moses, Peter Odemwingie and Nwofor in the second half and it was the latter who drilled home from an acute angle late in the game for Nigeria - who next face Greece in Pennsylvania on June 3.