Eoin Doyle wasted the hosts' first clear-cut opportunity in the opening exchanges, but was on hand on 19 minutes to set up James O'Shea who slid the ball past a despairing Barry Roche in the Shrimps goal.
Morecambe were nearly further behind later midway through the half, but for a last-ditch block to keep out Sam Morsy's effort.
The Lancashire club had struggled to threaten in attack, but they almost levelled the game before half-time when Ryan Williams's shot was kept out by Lee.
After the break, Chesterfield looked the more likely to score, with O'Shea being frustrated on three occasions in the opening minutes of the second half and Eoin Doyle twice being thwarted by Roche.
Morecambe's best chance of the game came with 17 minutes remaining, with Kevin Ellison dragging his left-footed strike narrowly wide.
However, Chesterfield had enough to hold on for victory and were unlucky not to have won by more in the dying stages when Morsy's fierce strike came back off the crossbar.