Glenn Whelan and Marc Wilson saw red after Oussama Assaidi had opened the scoring and the Magpies took full advantage with a goal-laden second half at St. James' Park.
Loic Remy scored twice in an ultimately convincing victory for Alan Pardew's men, who have now picked up 22 points from nine Premier League matches.
Yet Stoke was left fuming at referee Martin Atkinson, who handed red cards to Glenn Whelan and Marc Wilson – and also sent Mark Hughes to the stands – after Oussama Assaidi had given the visiting side a 29th-minute lead.
Remy saw a penalty saved by former Sunderland goalkeeper Thomas Sorensen - who replaced the injured Asmir Begovic - following Wilson’s exit, but found the net a minute later with the aid of a deflection.
Newcastle then made the most of the two-man advantage after halftime, with Yoan Gouffran scoring for the fifth successive home game, Remy grabbing his 10th league goal of the campaign and Yohan Cabaye beating Sorensen with a glorious first-time finish.
A second Newcastle spot kick was converted by substitute Papiss Cisse in the 80th minute to round off an utterly one-sided second period and a miserable afternoon for Stoke.
Hatem Ben Arfa returned to Newcastle's starting lineup for the first time since October in the absence of the suspended Cheikh Tiote.
Begovic was ruled out with a broken finger for Stoke, meaning Sorensen made his first Premier League appearance of the season in goal and Jack Butland returned from a loan spell at Barnsley to occupy a place on the bench.
After an eventful opening featuring long-range efforts at both ends, Stoke settled well.
Charlie Adam twice went close from distance either side of Newcastle's Cabaye trying his luck from 25 yards with a dipping strike that Sorensen palmed away somewhat unconvincingly.
Stoke then took the lead in the 29th minute as Assaidi cut in from the left before finding the top-right corner with a finish not dissimilar to his splendid winner against Chelsea earlier this month.
However, the visitors' joy was short-lived as Whelan picked up two bookings in quick succession, the first following an altercation with Cabaye and the second for tripping the Frenchman.
Stoke manager Hughes was sent to the stands for protesting against Whelan’s dismissal, and his side was remarkably reduced to nine men in the 43rd minute.
Wilson received a straight red card, having been adjudged to have pulled down Remy as the striker moved in on goal.
Sorensen dived to his right to keep out Remy’s resulting spot kick, but was powerless a minute later when a deflected effort from the striker found the net.
Gouffran capitalized on a poor punch from Sorensen three minutes after the break to continue his scoring run, although it appeared the ball may have gone out of play prior to Ben Arfa crossing from the right.
The excellent Ben Arfa twice struck the woodwork either side of Remy grabbing his second in the 56th minute. Davide Santon's cross from the left was flicked on by Sissoko and the former Marseille man made no mistake with a simple header at the far post.
Cabaye curled home from 20 yards 10 minutes later to enhance Newcastle's position and claim his fourth goal in as many matches against Stoke.
There was more joy to come for the home side as Cisse, another frequent scorer against Stoke, converted from 12 yards after Erik Pieters had upended Ben Arfa in the area.