Rangers' 100% record in the SPL came to an end after Inverness Caledonian Thistle earned a 1-1 draw at Ibrox, while Celtic beat St Johnstone.
Maurice Edu provided a first half lead but substitute Eric Odhiambo came off the bench to snatch a late leveller as the Highlanders maintained their unbeaten run on the road in the league which stretches back almost a year.
Earlier in the day a Niall McGinn double helped Celtic claim a comfortable 3-0 win over St Johnstone at McDiarmid Park and they now trail Rangers by one point.
Hoops' wide man Niall McGinn had the visitors ahead with just over a minute gone and four minutes from the end of a one-side half Emilio Izaguirre grabbed the second.
Saints defender Danny Grainger, booked for dissent following the opening goal, was given a second yellow by referee Murray for a foul on Anthony Stokes before McGinn scored his second from a Cha Du-Ri pass.
Nigel Hasselbaink's 15th-minute goal was enough to give Hamilton a 1-0 Lanarkshire derby win against Motherwell at Fir Park but once again a controversial refereeing decision was the main talking point of an SPL game.
Craig Thomson failed to produce a card after penalising Martin Canning for pushing Nick Blackman over in front of an empty goal and Motherwell's frustration was compounded when Tomas Cerny saved Tom Hateley's resulting penalty.
Hamilton battled their way through a second half of few chances to keep themselves off the bottom of the SPL.
Hibs forward John Rankin blocked Jon Daly's first-half diving header on the line but spurned the opportunity for further heroics as his 65th-minute penalty was saved by Dusan Pernis.
And Hibs' misery was compounded when Goodwillie latched on to a loose ball and visiting goalkeeper Mark Brown was caught in no-man's land as the United striker tucked in.
Jure Travner scored an injury-time winner to give St Mirren a long-awaited 2-1 victory over Aberdeen.
The midfielder drilled the crucial winner into the bottom-right corner after 92 minutes of play at New St Mirren Park to give his side only their second SPL victory of the season, their first since beating Hibernian in August.
Marc McAusland had opened the scoring for the hosts in the first half but his effort was cancelled out by Aberdeen's Rory McArdle just before the hour, and the teams seemed set to have to settle for a point apiece until the dramatic finish.
