It was bottom club Wrexham who were the happier of the two with the draw after being bombarded for long periods, before being given a lifeline after being awarded two penalties by Midlands official Andrew Hall.
Both spot-kicks were slotted home to give the visitors what could be a crucial point come the end of the campaign.
Morecambe started the game superbly with Wayne Curtis giving them a seventh minute lead. Carl Baker was the inspiration with a great cross from the right which flew across the Wrexham goal before Curtis bundled the ball past Gavin Ward from close range.
The visitors had played some neat football without causing Morecambe any problems, until they were gifted a penalty when Danny Adams brought down Stewart Nicholson in the area and Danny Sonner sent Shwan Jalal the wrong way from the spot.
Garry Thompson should have given Morecambe the lead again seconds later when put through, but with only Ward to beat, he stroked the ball into the sidenetting when it looked easier to score.
The Morecambe winger was then indebted to his own keeper Jalal for a superb save on 38 minutes to deny Wrexham a certain goal.
Chris Llewellyn's shot from the edge of the area hit the foot of the left-hand post, but the bell fell perfectly for Drewe Broughton whose first-time effort was somehow clawed away by the sprawling Shrimps keeper.
Morecambe took the lead for a second time on 51 minutes when Neil Roberts bundled the ball over his own goal line from Blinkhorn's backheel, but they were undone again when Blinkhorn was adjudged to have fouled in the area after a goalmouth scramble and substitute Michael Proctor smashed the ball down the centre of Jalal's goal for an equaliser 11 minutes from time.
Morecambe came close to pinching it in injury time with a David Artell header that flew inches wide of the bar, after Wrexham skipper Richard Hope had been sent off for committing a string of fouls.