The 2017-18 champions were in control of a one-sided contest before Wesley Fofana received his marching orders, leaving his team-mates to face an onslaught from PSG's four-pronged attack.
Icardi opened the scoring early in the first half and, after Neymar dinked in the second and goalkeeper Jessy Moulin bundled a third into his own net, the former Inter striker fired a second-half brace.
Not to be left out of the goal glut, Kylian Mbappe scored a sixth before Yohan Cabaye's late strike proved little consolation for Claude Puel's men, who bowed out with their tails between their legs.
Thomas Tuchel can reflect on another rampant attacking performance from his side, who have scored 29 goals in their last six games in all competitions, and remain very much in contention for silverware on four fronts.
Saint-Etienne were carved open with ease after two minutes when Thomas Meunier's slide-rule pass into the box found Icardi, whose angled shot Moulin would have saved had the visiting goalkeeper stood tall but it flashed over his crouching frame and high into the net.
Having earlier been booked for handball, Fofana was sent off after he caught Angel Di Maria's heels as the Argentina winger sprinted towards goal, and the 10 men were powerless to stop Neymar chipping Moulin for PSG's second after Di Maria threaded the assist.
6 - Paris have scored 6+ goals in 2 consecutive games in all competitions (6-0 v Linas-Montlhery & 6-1 tonight) for the 2nd time of their history, after September 1972 (2). Incredible. ✨#PSGASSE pic.twitter.com/8d6rmqY7ik— OptaJean (@OptaJean) January 8, 2020
Any hopes Puel had of rallying his team at the interval were spoiled when Mbappe's audacious backheel put Di Maria through for a cross that ricocheted off two defenders' shins before rebounding off the post, onto Moulin's legs and into the unguarded net.
Di Maria started the move that delivered PSG's fourth just four minutes after half-time, his pass releasing Mbappe whose cross deceived Moulin and left Icardi to fire into an empty net.
Saint-Etienne failed to cope with Mbappe's pace down the left and he burst clear before squaring to Icardi for the hosts' fifth shortly before the hour mark, and Icardi returned the favour 10 minutes later when he met Di Maria's long pass with a volley that played Mbappe in to score at close range.
Substitute Edinson Cavani had the ball in the net 10 minutes from time but he was flagged offside, compounding the Uruguayan's frustrations at missing out on much of a prolific period for PSG.
After Di Maria felled substitute Edmilson Indjai Correia in the box 20 minutes from time, Cabaye had a penalty saved by Sergio Rico but the midfielder met the rebound with a header that glided over the goalkeeper and into the net.
What does it mean? Icardi catching Mbappe
With few teams able to go toe-to-toe with PSG this season, their forwards are competing among themselves and Icardi's treble takes him to within two goals of catching Mbappe's tally of 19 in all competitions as the club's leading goal-scorer.
What a difference a year makes
It seems hard to believe that little short of a year ago Icardi was injury plagued, unsettled and facing an unclear future at Inter.
His revival under Tuchel has been spectacular and here he was back to his clinical best.
Juan to forget
On a night when Saint-Etienne barely got a sniff of the ball, Juan Bernat's overplaying at the back still threatened to allow them back into the game early on and he was wasteful with the ball going forward.
PSG will likely face a stiffer test when they entertain Monaco in Ligue 1 on Sunday, while Saint-Etienne are at home against fifth-placed Nantes.