Junior Lewis had a good match in his new role as centre-forward and his pass to Green saw the City midfielder nod just wide of the near post in the opening minutes.
But Chesterfield gradually gained the upper hand even though they could not produce any real shots on goal.
In the 18th minute, Shane Nicholson's mistimed header conceded a corner to City, but the Chesterfield defender's blushes were saved when Leon Cort could only slice a shot into another Spireites defender.
Sammy Clingan, who impressed on his debut, shot over from 25 yards in the 26th minute as Chesterfield piled more pressure on City's defence.
In the 32nd minute, Boaz Myhill denied Wayne Allison with his feet after City's defence fell asleep and allowed him to run clear.
Four minutes later, Jason Price did well to turn and control on the edge of the area, but he couldn't keep his shot down.
Deep into first-half injury-time, Gareth Davies missed a glorious chance to score after the Tigers let him slip through. With the goal at his mercy he shot yards out.
Green got City's first shot on target in the 48th minute with a 20-yard drive which Carl Muggleton did well to beat away.
Seconds later the Tigers had a real scare when Myhill somehow managed to claw Ian Evatt's shot off the line.
Mark Stallard had the ball in the net a minute later, but his effort was ruled offside.
Stallard headed inches wide in the 58th minute when it seemed easier to score and two minutes later, Allison shot just over the bar from eight yards out.
In the closing minutes, a looping header from Evatt was well tipped over by Myhill, who then had to save at his feet amid chaos in the Tigers box following a corner.
But the Tigers stood firm and it became clear that despite all their dominance, it was not to be Chesterfield's day.