Celtic won the title, finishing three points ahead of Glasgow rival Rangers when it at Dundee United, 1-0, on Thursday and Rangers fell at Aberdeen, 2-0.
The drama extended into the second half of the two games before Celtic eased ahead for its third straight championship and 42nd league title overall.
Dutchman Jan Vennegoor of Hesselink scored on a header in the 72nd minute to give Celtic the win.
Less than 10 minutes earlier, Rangers had fallen behind on Lee Miller's goal. Aberdeen got a second goal from Darren Mackie after 77 minutes to spoil Rangers' hopes.
Rangers went into last week chasing four trophies. It lost to Zenit St. Petersburg, 2-0, in the UEFA Cup final. It saw its edge over Celtic evaporate when it was tied by Motherwell, 1-1.
It has already won the Scottish League and is favored to win the Scottish FA Cup Saturday when it meets Queen of the South.
American DaMarcus Beasley didn't play in Thursday's game for Rangers.