A Celtic victory and title celebrations at Rangers' home stadium would have been the final indignity of a harrowing season for the Glasgow club, who have been docked 10 points for going into administration amid large debts.
They started the day 21 points behind the champions-elect but the gloom surrounding Ibrox in recent weeks was lifted when Sone Aluko put Rangers ahead with a fine solo goal after 11 minutes.
Their fans were lifted even further after second-half strikes from substitute Andy Little and Lee Wallace put them 3-0 ahead.
Celtic struck back with two late goals as captain Scott Brown scored from an 89th minute penalty after Carlos Bocanegra was sent off for a foul on Georgios Samaras before Thomas Rogne powered in a header in stoppage time.
Those goals though were little consolation for the visitors who had Cha Du-Ri sent off for hauling down Wallace after 29 minutes and midfielder Victor Wanyama sent off for a two-footed tackle on Steven Whittaker after 57 minutes.
Celtic manager Neil Lennon was also ordered from the dugout at the start of the second half for abusing the match officials, but there is little doubt Celtic will be celebrating the title shortly, even though their party was delayed on Sunday.
Celtic, who have 75 points from 31 matches and are 18 clear of Rangers, can clinch their 43rd league title next week when third-placed Motherwell play Rangers and they host St Johnstone.
Rangers, champions for the last three seasons, have won the title 54 times but at the moment are more pre-occupied with who might take over the club, which owes millions in unpaid taxes and other debts.
On Sunday, reports said a Singaporean consortium have become the fifth group to show an interest in taking over the stricken giants, who look poised to finish as runners-up.
Despite that, they are set to be denied European competition by UEFA next season for falling foul of their financial fair play rules.
Administrators hope new owners can be in place by the end of the season.
