Sammy McIlroy's men had not lost two games on the trot prior to the losses
But Baker's tenth goal of the season earned the point.
Morecambe's turnaround was inspired by the introduction of Garry Thompson from the bench at the break.
Thompson's pace changed the game and he set up Baker's goal with a smart free-kick and was also inches away from winning the match after a run and shot which flew just wide of the post.
The Shrimps had fallen behind to the first shot of the game on 28 minutes when Richard Butcher lobbed Shwan Jalal in fine style after a bad error from Stewart Drummond gave the ball away on the edge of his own box.
As the interval approached Morecambe got more into the game with Michael Twiss a threat, although Felix Bastians could have put County two clear when he shot horribly wide after Jalal flapped badly at a corner.
Thompson's introduction changed the face of the game.
The winger immediately ran and crossed for Twiss to volley horribly wide from a good position and County were on the defensive.
Their chances were few and far between in the second period as Morecambe's defence, marshalled superbly by David Artell and Jim Bentley kept the Magpies out.
And when Thompson delivered his ideal cross, Baker was on hand to slam home.