After going down to an early Dean Morgan goal, Stoke's comeback came courtesy of Luton's Steven Howard.
The forward left his side in the lurch on the 26th minute when he was dismissed for an alleged spitting offence.
An angry Luton boss Mike Newell was eager to spring to his player's defence.
He said: "I know Steve well and I only had to look him in the eye to know he hadn't done it.
"The referee said he spat but he is wrong and that has cost us the game.
"I think we were unlucky as even with 10 men we still looked the better side.
"We want to show people that we are here to play good football and that we won't just be rolled over."
And that was certainly the case for much of the early action as Luton had the home side on the back foot.
And relieved City boss Johan Boskamp was left thanking his lucky stars for Brammer's injury-time heroics.
He said: "For me he can do that every game, it was a very good goal.
"I am extremely happy, winning for the first time at home, but I thought Luton were the better side.
"We just didn't play football much of the game whereas they did.
"Only when we equalised did we start playing well and I think the fans responded to that."
Luton dangerman Howard gave the Potters defence an early scare when he got on the end of an Ahmet Brkovic centre.
Although Howard's resultant header lacked accuracy, the striker's aerial presence proved the undoing of City's defence in the ninth minute.
The towering frontman nodded the ball down in the City box and when John Halls failed to clear, Dean Morgan pounced.
Halls' hashed clearance fell into the path of the advancing Morgan who thumped the ball past the flapping City keeper.
After an opening 20 minutes of playing havoc in the City box, a moment of madness from Howard threw Luton's early lead into jeopardy.
Andy D'Urso gave Howard his marching orders after he spotted the striker allegedly spitting at City defender Carl Hoefkens.
For the remainder of the half the host's numerical advantage was apparent as Stoke poured forward.
Although Stoke went into the half time break trailing it wasn't down to a lack of effort.
The energetic Brammer signalled City's renewed interest in the game with two thunderous long-range strikes.
With all caution thrown to the wind in the second half, Stoke's appetite for an equaliser had the Hatters rattled.
And it only took the home side 17 minutes of second-half football to get back into the game.
The jittery Luton defence failed to deal with a Kevin Harper cross and, with Stoke piling forward, there was queue of players waiting to pounce.
It was Potters full-back Marlon Broomes who accepted Luton's invitation to shoot, poking the ball into the bottom corner.
And Stoke continued to bombard the Luton goalmouth in search of the winner.
And Brammer almost inflicted Luton's first Championship defeat when his thunderous 30-yard drive struck the bar.
But there wasn't much that Luton keeper Marlon Beresford could do when Brammer let rip for a fourth time.
The midfielder's scorching long-range drive ended Luton's unbeaten Championship run and clinched all three points for the home side.