Nacho Novo's first goal since early March gave Rangers the SPL title, as Hibs finally clinched third spot and a place in next season's Uefa Cup.
Motherwell's late goals at Fir Park allowed Rangers to finish a point clear of rivals Celtic.
The goal came after 59 minutes, when Novo's shot was deflected into the net by Gary Caldwell.
Novo hit the post early on after Simon Brown misjudged a pass, allowing the Spanish striker to fire in a shot.
Rangers had arrived at Hibernian knowing they had to win to have any chance of snatching the title from Celtic on the final day of the season.
As Rangers and Hibernian played out a scoreline that would also ensure Uefa Cup football for the home side next season, thousands of ears instead became glued to radios in the hope of good news.
Hibernian had been keen to underline the fact that they had plenty to play for as well and started strongly.
Derek Riordan and Garry O'Connor both fired in early testers and the latter was only inches away from opening the scoring in the 10th minute.
That was via a flicked header from Stephen Glass' free-kick from the right that saw the ball skim over Ronald Waterreus' crossbar from fewer than six yards out.
A Rangers response was required and within a minute Novo almost opened the scoring.
Home goalkeeper Simon Brown was the man who had put his side in jeopardy by mis-judging the bounce of a long ball forward from Alex Rae.
Novo was on to it in a flash but when he attempted to find an empty net from a tight angle on the right he ended up rolling the ball against the near post.
The half hour mark was greeted with an increase in the volume levels from both sets of supporters but only because news of Chris Sutton's opener at Fir Park had reached the capital.
Tackles had already been flying in by this point but the play became even more frenzied, with Alex Rae often in the thick of the midfield action.
Gary Smith made a vital block to deny Thomas Buffel, after Dado Prso had headed the ball into his path.
Within a few minutes of the re-start, Prso had sent Buffel through with a flick but the Belgian was denied by a superbly-timed challenge in the box by Steven Whittaker when there was zero margin of error.
The hour mark was fast approaching but so, the Hibs defence found, was Novo as a passing move involving Prso and Buffel found the Spaniard on the right of the box.
The shot that followed was not the sweetest he has ever struck but goalkeeper Brown could only get a touch that did not prevent it bouncing over the line.
The game petered out after that as it became apparent that the scoreline would suit both side's requirements.
All Hibs wanted was no news of further Aberdeen goals and indeed none came.
What information did arrive was remarkable nonetheless and as soon as the final whistle was blown there was no hesitation from the Rangers players or their fans.
They knew that fortune had favoured them and were intent on making the most of celebrating the fact.
Hibernian: Simon Brown, Whittaker, Caldwell, Smith, Ian Murray, Sproule (Shiels 65), Scott Brown, Beuzelin (Antonio Murray 74), Glass, O'Connor (Konte 68), Riordan. Subs Not Used: Alistair Brown, Hogg, Murphy, Morrow.
Booked: Beuzelin, Ian Murray, Riordan, Scott Brown.
Rangers: Waterreus, Ricksen, Andrews, Kyrgiakos, Ball, Arveladze, Ferguson, Alex Rae, Buffel, Prso, Novo. Subs Not Used: McGregor, Thompson, Malcolm, Burke, McCormack, Steven Smith, Lovenkrands.
Goals: Novo 59.
Ref: K Clark