Pilgrims keeper Romain Larrieu was the hero as his superb saves earned the Devon outfit their first away point of the season.
As Chesterfield made it four draws out of four starts Larrieu denied them time and time again.
In an inspired first-half display the giant 27-year-old Frenchman was all that stood between Chesterfield and a commanding lead.
On 27 minutes he produced a world-class effort to parry away Mark Hudson's 18-yard drive.
Ten minutes later he dashed from his line to deny Glynn Hurst in a one-on-one and then sprinted back to fist away a Hudson header.
But he could do nothing on 50 minutes when his defenders let him down.
An innocent free-kick was headed on in the box and Plymouth stood and stared as Chris Brandon nipped in at the far post to stab the ball home from close range.
Pilgrims boss Paul Sturrock threw on striker Micky Evans and went to 4-3-3 and his gamble paid almost instant dividends.
Within minutes Ian Stonebridge had converted Jason Bent's free-kick only for his effort to be ruled out for a marginal offside.
But on 66 minutes David Worrell's right-wing cross found David Friio unmarked in the box and from 15 yards the midfielder looped a header over the stranded Carl Muggleton.
From then on it was Muggleton's turn to produce the goalkeeping drama as the Pilgrims threatened a second.
He produced a superb diving save again from Friio as Chesterfield struggled to match the visitors' rhythm.
There was still time for Larrieu to underline his man of the match performance with a save in the dying minutes from Hudson.
Afterwards Sturrock admitted: "In the end the goalkeepers came out of top but I am disappointed we didn't go at them with more venom until we were a goal down.
"Even after we'd equalised we didn't go for the jugular." Chesterfield boss Roy McFarland, admitted: "A draw was a fair result and Plymouth are a decent outfit.
"After all these draws we're desperate to win a game and I thought we just did enough today to snatch one, although we are never going to be prolific goalscorers."