Jim Harvey's side enjoyed a dream first half to lead 3-0 at the break.
The fun began after 12 minutes when Michael Twiss opened the scoring with his fifth goal of the season. It certainly wasn't the hardest hit shot he's ever struck but the ball squeezed under Alan Julian's dive and ended up in the back of the net.
Julian was picking the ball out of the back of the net again 12 minutes later after a superb Morecambe second. Wayne Curtis was the creator on the left-hand side as he held the ball up perfectly waiting for the run of Garry Hunter and the young midfielder steamed through the middle of the Boro defence to side-foot his effort into the bottom right-hand corner.
Then to make maters worse for Graham Westley's side the Shrimps added a third five minutes from the break. Twiss was the architect with a defence-splitting ball for Gary Thompson. Julian saved the first effort but the ball rebounded back off the Morecambe striker and into the net.
The second half saw the Shrimps happy to sit back and defend and Stevenage almost made them pay straight after the restart when Danny Bulman's 30-yard low drive forced Ryan Robinson into an excellent save low to his left.
The visitors did get off the mark however close to the hour when Boro's star man George Boyd found space on the right and his low cross was turned in by Jon Nurse.
Any hopes the visitors may have had of a comeback were then dashed when, with 20 minutes to go, left-back Justin Gregory was sent off for his second yellow card after wrestling Danny Carlton to the floor.
And as Stevenage pressed forward the gaps continued to appear for the Morecambe forwards and they took advantage.
On 90 minutes Curtis went close after being played through by another superb Michael Twiss ball but in the fifth minute of injury time he made no mistake when through on goal again to drill the ball past Julian to cap a fine win.