Steve Morison's treble earned Stevenage their first point of the season.
Morison opened the scoring after 41 seconds when he converted Luke Oliver's cross, but a Michael Twiss header brought Morecambe level.
Stevenage regained the lead immediately when Morison volleyed home Steve Guppy's pass but Wayne Curtis squared for Twiss to make it 2-2.
Curtis set up Danny Carlton to put Morecambe ahead for the first time but Morison's volley earned Borough a draw.
Morecambe: Robinson, Yates, Meadowcroft, Blackburn, Howard, Craig Stanley, Thompson, Hunter, Curtis, Twiss, Carlton.
Subs Not Used: Rigoglioso, Brannan, David McNiven, McLachlan, Davies.
Goals: Twiss 24, 48, Carlton 50.
Stevenage: Julian, Fuller, Goodliffe, Oliver, Nutter, Dobson (Thorpe 74), Miller, Hicks (Henry 67), Guppy, Boyd, Morison.
Subs Not Used: Gaia, Stamp, Wright.
Booked: Hicks, Oliver.
Goals: Morison 1, 26, 60.
Ref: A Haines (Yorkshire).