Before the match Stevenage knew the victory would lift them above the visitors, who came to Broadhall Way in second place in the league.
But it was Morecambe who made a brighter start and who created two good chances inside the first ten minutes when both Stuart Barlow and Gary Thompson tested home keeper Alan Julian.
The Shrimps continued to threaten and though they had gone ahead from 21 min when a free-kick whipped in by Thompson came back off the post and out to safety.
Stevenage came closest with an effort from Jon Nurse before the striker found the net on 35 minutes.
Nurse showed great calmness as he controlled a high through ball over the Morecambe defence and lobbed keeper Stephen Drench who was caught off his line.
The goal spurred Boro on and Adam Miller could have added a second before the break when he saw an effort from a tight angle well saved.
The second period proved to be more open with both sides having clear chances.
Nurse and Dino Mamria both had two good efforts apiece for Stevenage, while Thompson saw a cross come back off the top of the bar, while he also forced a diving save from keeper Julian with an effort at the far post which looked to be heading in.
Stevenage ran the clock down in the final minutes and on the referee's final whistle were jubilant at the win which puts them third, while Morecambe were disappointed that they hadn't taken a point from the game.