Baker popped up in the 90th minute to slide home a right-wing cross from the excellent Garry Thompson to clinch an exciting game, which could have gone either way.
In the end it was the Shrimps' more clinical finishing that proved vital as Bradford missed several excellent chances to win the game. Their failure to take them means they have now lost their last five games much to the annoyance of boss McCall.
The Bantams thought they had the perfect platform to end their recent barren run when they took the lead two minutes before the break.
Nicky Law swung in a free-kick and defender Mark Bower was unmarked in the box as he directed a header into the top right-hand corner of Joe Lewis' goal.
But Morecambe stormed back into the game in the second half and levelled on 64 minutes through a well worked free-kick.
Craig Stanley laid the ball of sideways to man of the match Thompson who broke free from his marker to shoot past Rhys Evans.
From there on both sides had chances to win the game, with City looking the more likely to take the points.
Omar Daley looked sure to score after outpacing former Huddersfield full-back Danny Adams, but failed to hit the target from six yards out when he should have done better.
Then with time running out the experienced Barry Conlon was denied a goal by a superb save from Lewis, after a neat turn and shot just inside the box.
The giant on-loan Norwich keeper proved to be Morecambe's hero two minutes from time with a stunning double save to block from Guylain Ndumbu-Nsungu and Kyle Nix, before the Shrimps took the points after a flowing counterattack.