The visitors started brightly and Steve Simonsen twice denied Alex Frutos before Bangoura calmly finished from Paul Gallagher's through-ball.
Gallagher's curling cross bounced back off the bar before Darel Russell made it 2-0 after Alan Blayney blocked Mamady Sidibe's close-range effort.
Victory was sealed when Bangoura rose unmarked to nod John Halls' cross past Blayney at the near post.
Brighton boss Mark McGhee said:
"We gifted them a ridiculous goal. We gave them too much space after giving the ball away and after that couldn't get back into it. "We were in control of the game dominating it completely and at half-time I was happy because we'd done everything we planned to do.
"We're good at looking to the next game. We won't dwell on this. I'm confident we'll beat Crystal Palace."
Stoke: Simonsen, Buxton, Hoefkens, Duberry, Halls, Gallagher (Henry 86), Brammer, Russell, Sigurdsson (Chadwick 45), Sidibe, Bangoura (Mbuyi 88).
Subs Not Used: de Goey, Wilkinson.
Booked: Russell, Bangoura, Brammer, Duberry.
Goals: Bangoura 35, Russell 68, Bangoura 75.
Brighton: Blayney, Hart, Butters, McShane, Reid, Carole, Hammond, Nicolas, Frutos, Kazim-Richards (Turienzo 72), Robinson (McPhee 64).
Subs Not Used: Mayo, Dodd, Chaigneau.
Booked: McShane.
Att: 15,274.
Ref: K Wright (Cambridgeshire).
MMIX
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