Karl Hawley had the first chance after 16 minutes when he turned and had a shot punched away by Chesterfield 'keeper Tommy Lee from close range.
Barry Nicholson, making his home debut after a free transfer from Aberdeen, fired a cross over from the left and Hawley had another shot saved by the keeper with his legs.
After half an hour Lloyd Kerry, from outside the box, hit a right foot shot which Andy Lonergan did well to save and seconds later Darren Carter hit a shot just over the bar.
Mellor had a header saved and then in the 37th minute made it 1-0 when a Ross Wallace left-wing cross was fired by Hawley at goal but the keeper parried and Mellor buried the rebound with his right foot from close range.
Chesterfield brought on Darren Currie for Gregor Robertson at half time and Jamie Ward squandered a great chance in the 50th minute when he shot wide of the right hand post.
Derek Niven replaced Kerry and Jamie Lowry had a left-foot shot from outside the box which was saved by the Preston keeper who did well to dive to his right.
Paul Harsley hit the crossbar with a right foot shot from outside the box with seven minutes to go but in the third minute of added time Carter crossed from the right and Mellor slid the ball into the bottom right corner from close range to make it 2-0.