The Frenchman emerged from a five-game barren run with a double in a remarkable game which saw Glenn Whelan and Marc Wilson pick up red cards, Potters manager Mark Hughes sent to the stands, two goals and a saved penalty before the half-time whistle had sounded.
Oussama Assaidi had fired the visitors into a 29th-minute lead with a superb curling effort as Alan Pardew's side failed to hit the heights until a dramatic conclusion to the first half.
But Whelan departed prematurely five minutes before the break for a second bookable offence, and Wilson joined him within three minutes for hauling down Remy inside the box.
The Frenchman saw his spot-kicked saved by goalkeeper Thomas Sorensen, but dragged his side back into the game seconds later with a deflected effort.
However, the home side ran riot after the restart as Yoan Gouffran, with his fifth goal in as many home games, Remy, Yohan Cabaye and substitute Papiss Cisse secured a seventh Barclays Premier League win in nine attempts for the Magpies in front of a crowd of 51,665.
Newcastle's recent success has been founded on the platform provided by midfield enforcer Cheick Tiote, who has returned to something like his best form.
His absence through suspension against the Potters was a blow, but just how much they would miss him became abundantly apparent at a very early stage.
Charlie Adam was gifted acres of space in front of the Magpies' back four with Vurnon Anita and Moussa Sissoko, playing the holding roles in a 4-2-3-1 formation, unable to cut the supply lines.
After an encouraging start by the home side, during which Sissoko, Hatem Ben Arfa and Gouffran all went for goal from distance, it was the visitors who gained a measure of control.
Newcastle full-back Mathieu Debuchy was fortunate to see his sliced clearance from Adam's driven cross fly across his own goal and out for a corner, and the Scotland international only just missed the target with two efforts from just outside the penalty area in the space of eight minutes.
However, keeper Tim Krul was finally beaten with 29 minutes gone when Assaidi cut inside from the left and curled an exquisite right-foot shot across the Dutchman and inside the far post to give the visitors a deserved lead.
Pardew's men were labouring, but were given a shot in the arm five minutes before the break when Whelan, who had earlier been booked after fouling Sissoko, clattering into Cabaye and kicking the ball away, picked up a second yellow card for a foul on the former Lille midfielder.
What was to follow was astonishing as Newcastle stepped up a gear and Stoke imploded.
There were just two minutes of the half remaining when Wilson felled Remy inside the box and as last man, joined Whelan back in the dressing room, much to the fury of Hughes, who was sent to the stands for his protests as his side appealed in vain for a penalty at the other end for handball against Mike Williamson.
Sorensen repeated his heroics in the shirts of Sunderland and Aston Villa, for both of whom he saved Alan Shearer penalties at St James' Park, by diving to his right to keep out Remy's spot-kick.
However, the Frenchman made amends within seconds when he sent a deflected shot past the Dane to level.
Hughes replaced goalscorer Assaidi with defender Andy Wilkinson at the break as Pardew sent on striker Shola Ameobi for Anita, and his side took the lead within three minutes when Stoke failed to clear Ben Arfa's cross - the ball looked to have crossed the goal-line before the Frenchman delivered it - and Gouffran dispatched it into the bottom corner.
The 11 men were running riot and extended their lead with 56 minutes gone when Sissoko flicked on Davide Santon's cross for Remy to convert at the far post.
Ben Arfa, who had earlier struck the foot of the upright, smashed a 58th-minute shot against the crossbar after a mesmerising run which took him past three Stoke defenders, but compatriot Cabaye's lovely 66th-minute finish from Debuchy's pull-back further extended the lead.
There was still time for Cisse to claim his first league goal of the season from the spot with 10 minutes remaining after full-back Erik Pieters had tripped Ben Arfa with Stoke in disarray with referee Martin Atkinson waving away a series of appeals for further penalties as time ran down.