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The reigning champions closed the gap on Lille, who could only draw 1-1 with Montpellier on Friday, thanks to Icardi's 95th minute header which saved a win that had looked to have slipped away.
Kylian Mbappe struck twice in quick succession to put PSG ahead after Denis Bouanga had given the away side a shock 78th-minute lead by guiding home Miguel Trauco's cross.
Romain Hamouma thought he had grabbed an improbable point for Saint-Etienne in the second minute of added time when Bouanga's saved shot fell at his feet in front of a gaping goal, giving him an easy tap-in.
But Icardi capped a thrilling last quarter when he met fellow substitute Angel Di Maria's whipped cross with a perfect header three minutes later to spark wild celebrations among the PSG players.
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PSG, who had lost their previous three league home matches, are one of four teams in an exciting French title race, with both Monaco and Lyon also having the chance to get closer to Lille later on Sunday.
Third-placed Monaco, who have won their last three Ligue 1 matches scoring 11 goals, can move to within two points of Lille with a win at struggling Bordeaux.
Lyon are a point behind Monaco in fourth and take on relegation-threatened Nantes in Sunday's late match.
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