First-half goals from Zlatan Ibrahimovic and Ezequiel Lavezzi at the Parc des Princes looked to have put PSG on course for a victory which would have put them back on top of the league for the first time since December.
But injuries to Yohan Cabaye, Marquinhos, Serge Aurier and Lucas Moura left the champions to finish the game with nine men, and they wilted in the face of visiting pressure.
Emiliano Sala reduced the arrears with two minutes to play before a stoppage-time free-kick from Herve Bazile beat Salvatore Sirigu and snatched a point.
PSG remain a point off Lyon, who can extend their advantage at Lorient on Sunday.
Blanc may be forced to shuffle his pack when runaway Premier League leaders Chelsea visit the French capital on Tuesday while his players will be in desperate need of a psychological lift.
Things had looked rosy early on for PSG as their early breakthrough came when Cabaye swung the ball out to right to Aurier and the full-back's cross was met by the onrushing Ibrahimovic, who stuck out his right foot to volley home from six yards.
Cabaye stung the palms of Remy Vercoutre, before the former Newcastle United man hobbled off injured to be replaced by Adrien Rabiot.
As they dominated the majority of play, a second PSG goal arrived five minutes before the break. Lucas glided through the Caen defence and teed up Lavezzi on the left, who finished emphatically into the far corner.
Blanc was forced into a second change at half-time as David Luiz replaced Marquinhos, suffering from a thigh injury, but it did not appear to limit their momentum as Lavezzi forced Vercoutre into a smart fingertip save.
Having made all three substitutions, PSG were reduced to 10 men when Aurier was stretchered off with a thigh injury, before Lucas followed the Ivorian from the field, having attempted to struggle on.
The game swung on its head as Caen unsurprisingly threw bodies forward and the numerical advantage paid dividends when Sala bundled home a difficult bouncing ball in the 88th minute.
And the comeback was complete in the first minute of injury-time. Nicolas Benezet was tripped on the edge of the area by Ibrahimovic and Bazile fired the resulting free-kick past a helpless Sirigu much to delight of the visitors.
Blanc will now have his fingers crossed that medical results come back with good news ahead of another clash with Jose Mourinho's men.
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