Blinkhorn made it six goals from the last seven games when he headed home Wayne Curtis' deep cross.
The struggling Daggers looked set to secure a point after keeper Ed Thompson marked his Football League debut with a penalty save from Carl Baker 20 minutes from time but John Still's side could not hold on.
Dagenham started well with new loan signing Ryan Hall causing Morecambe early problems.
On 15 minutes he fired a shot which deflected inches wide of the right-hand post before the same player headed the resulting corner inches over from close range.
At the other end Morecambe were denied by the impressive Jon Boardman and Anwar Uddin until Stewart Drummond wasted a glorious chance on the half-hour when he rose unmarked only to head Baker's corner over from close range.
The second half saw plenty of effort but little fluid football on a sticky pitch.
For Morecambe, Garry Thompson's first touch let him down when played through by Blinkhorn, while at the other end the diving Shane Huke should have hit the target from an excellent Hall corner which the home defence failed to deal with.
Dagenham had another golden chance when Ben Strevens side-footed over from close range after getting on the end of Simon Grand's desperate clearance before the Shrimps wasted an opportunity to go ahead from the spot after Boardman had needlessly bundled over Blinkhorn.
Dagenham came back with substitute Jamie Taylor forcing new Morecambe keeper Shwan Jalal into an excellent save from a long-range effort with two minutes to go.
But with the Daggers looking set for an excellent point, Blinkhorn was left all alone in the box to direct a downward header past young keeper Thompson to give Morecambe their fifth win in the last six games.