Although Scott McDonald gave the hosts an early lead, Liam Boyce levelled matters four minutes before the break to keep the visitors six points clear of Well with just three matches remaining.
Motherwell dominated the early stages with Marvin Johnson and McDonald both having efforts saved by Mark Brown.
And the hosts duly took the lead in the 19th minute when McDonald netted at the far post as he swept home Conor Grant’s assist.
County improved as the half continued and were level on 41 when Boyce located the bottom right-hand corner of the net following Raffaele De Vita’s pass.
County started the second half the stronger with Scott Boyd firing inches wide for the visitors, while Michael Gardyne had an effort saved.
At the other end, Grant tested Brown from outside the box, while Stephen Pearson was also denied by the visiting keeper.
County could have won it in second half injury time but a Jackson Irvine header flew wide of a post.
However, the point will benefit the visitors more than Motherwell whose chances of putting pressure on Saturday’s opponents slipped through their fingers on home soil.