The Hoops fell two goals behind at Fir Park Stadium earlier today thanks to strikes from John Sutton and Zaine Francis-Angol, before drawing level through Anthony Stokes and Georgios Samaras just short of the hour mark.
Leigh Griffiths looked to have won it late on for the champions, but John Sutton struck in the closing stages to ensure that the points were shared.
Things were made difficult for the home side, however, when the same player was sent off five minutes later after a second yellow card, but they doubled their lead through Dale Carrick in injury time.
Kilmarnock have gone down 2-1 at home against Partick Thistle, with Vitalijs Maksimenko opening the lead for the home side in the 54th minute, before Kallum Higginbotham equalised just three minutes later.
The Jags secured all three points with five minutes to go when Aaron Taylor-Sinclair nodded the ball in at the near post.
Elsewhere, St Mirren saw off Hibernian 2-0, the home side scoring the day's quickest goal in just 37 seconds thanks to Kenny McLean's strike, before the scorer turned provider for his side's second goal, assisting Paul McGowan in the 14th minute.
The Buddies hung on for the win despite having Jim Goodwin sent off on the half-hour mark.
Results in full: Motherwell 3-3 Celtic, Hearts 2-0 Ross County, Kilmarnock 1-2 Partick Thistle, St Johnstone 2-0 Dundee United, St Mirren 2-0 Hibernian