Pools were by far the better side for around 70 minutes, having led since first half stoppage time.
But Pemberton's switch from 4-4-1-1 to 3-5-2 paid dividends, gave Town forward momentum and allowed Brad Barry to get forward to score a vital equaliser.
The early signs were promising for Town, some nice passing football creating first a crossing chance for Lee Shaw that he wasted, then a shooting chance that was blocked.
Hartlepool's first effort came on 10 minutes, Josh Hawkes' dipping drive well taken by Callum Burton.
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Kyel Reid's first touch came under scrutiny in the opening stages, failing to control the ball and ending what was up to that point a clever short corner routine, then losing possession and allowing Pools to counter, Ryan Donaldson's shot mercifully tame.
With Levi Amantchi struggling to get hold of the ball up front on his own, Town were without an outlet and found themselves under increasing pressure.
Hawkes clipped just wide of the post in Pools' best chance of the opening half an hour.
They came even closer when the Spireites failed to deal with a corner, Donaldson blasted the ball against team-mate Carl Magnay and it bounced the wrong side of the post.
Town fell further and further under the cosh, Hartlepool playing the better stuff and looking by far the more dangerous side.
But as the half neared its conclusion, Chesterfield rallied a little, Jonathan Smith slicing a shot well wide before Joe Rowley beat a defender and saw his shot deflect off another and over the top.
That resurgence was short lived, Pools taking the lead on the stroke of half-time when Liam Noble strolled past Rowley and, aided by a slip from Jerome Binnom-Williams, played the ball into Luke James, who stroked it under Burton.
James went hunting for his second five minutes after the interval, this time Binnom-Williams was in place to get a foot in and deflect the shot over.
A double substitution and that change of formation almost paid instant dividends. Shaw, who had joined Amantchi up top, nodded the ball on for himself and scampered into the box before being bundled over as he shaped to shoot. Referee David Richardson turned down the penalty appeals of the incandescent Town players.
What would have made the mood inside the Proact worse was if Pools had scored on the counter straight after the controversy, but Niko Muir blasted over to waste a good chance.
Luke Rawson hadn't been on the pitch a minute when he was handed a golden chance to level, Weston swinging a ball into the box, Brad Barry heading down to the teen striker who was all alone at the back post but somehow hooked over from four yards.
The youngster almost made amends when he turned brilliantly to run onto Smith's pass and get clear of the defence, but his shot slid past the far post.
A goal was coming and with 15 minutes left it finally arrived.
Shaw's cross from the right wasn't cleared by the Pools defence and Barry was there to fire home from 12 yards through a crowd.
Town looked dangerous going forward but had to be wary of the counter attack in the final stages, although bar a header at each end from set-pieces, neither came close to a winner.
Chesterfield: Burton, Barry, Binnom-Williams, Hollis, Evans, Smith, Weston, Reid (Sharman 55), Rowley (Beestin 55), Shaw, Amantchi (Rawson 68). Not used: Anyon, Weir.
Hartlepool United: Loach, Richardson, Kitching, Rodgers, Anderson, Magnay, Noble, Donaldson, Hawkes (Featherstone 87), Muir, James. Not used: Kioso, Newton, O'Neil, McLaughlin.
Goalscorers: Barry 75; James 45
Yellows: Shaw 23; Donaldson 90
Referee: David Richardson. Assistants: Robert Wainwright, Alex Gray.
Attendance: 4,752 (575 away)