In doing so they made Norwich City relegation favourites, because their only hope of avoiding the drop now would be to win at Charlton Athletic and hope that Plymouth Argyle beat Barnsley.
The visitors had the best of the early exchanges and Jason Shackell was forced to rescue the Canaries when he blocked Long's goalbound shot.
After 21 minutes the lively Cody McDonald was brought down by Liam Rosenior who was booked, but Sammy Clingan hit the side-netting with the resulting free-kick.
After 32 minutes David Carney went close with a long-range effort.
Alan Gow thought he should have had a penalty when Andre Bikey blocked his run, but referee Clive Oliver thought differently.
Three minutes into the second half Gow came close to opening the scoring with a curling shot that went the wrong side of the post.
Mr Oliver then upset the home fans by penalising McDonald when it appeared he had been the victim of obstruction by Bikey.
Norwich were undone in the 68th minute when Jimmy Kebe crossed from the left and Long headed in at the far post.
The same double act produced the second goal ten minutes later when another left-wing cross from Kebe was headed in at the far post by Long.
After the whistle the City players came back onto the pitch for a lap of honour for their fans, many of whom were still in the ground.
It remains to be seen how many of the current players will still be at Norwich next season, or which league they will be playing in, but it looks very much like being League One.