Both sides scored five tries in a hugely entertaining match which would left have the 6000 fans who packed into Rodney Parade surprised that neither of these sides had enough quality to qualify for the final eight.
Home outside half Jason Strange's 14 points with the boot help secure the victory for the Gwent club.
Newport set their stall out early, and Forster got his double in the opening quarter, and when Canadian prop Rod Snow added a third score, Newport were flying.
But Edinburgh stuck back with tries from Conan Sharman, Allister Hogg and Craig Smith - but Chris Paterson failed to convert on each occasion.
Strange re-established the home side's lead to 32-18 after the break with a 13 point kicking streak via two penalties, a try and a conversion.
But Edinburgh fought their way back in the game to ensure a thrilling climax with converted tries from centre Tom Philip and replacement full-back Brendan Laney.
But Newport were not to be denied in front of their home fans, and a late penalty goal from Strange and an injury time, and a try by Ofisa Tonu'u secured the victory.