Benteke broke the deadlock from the penalty spot with his 15th goal of the campaign and N'Zogbia made the points safe with a superb free-kick.
Ashley Westwood's late own-goal could not prevent Villa's first win in nine league games and ended a run of four successive home league defeats.
Paul Lambert's side also looked more secure in defending set pieces than in recent games with Ciaran Clark impressive.
But West Ham have now lost five successive away games and are in danger of being sucked towards the relegation zone.
Villa started brightly and Andreas Weimann missed a golden opportunity to put them ahead after less than two minutes.
Hammers keeper Jussi Jaaskelainen failed to hold a dipping shop from Benteke and the rebound fell to Weimann unmarked six yards out.
But the Austrian placed the ball wide of the far post with the goal at his mercy and held his head in his hands.
Weimann then raced onto a flick from Benteke but Hammers defender James Tomkins was alert to the situation and tidied up.
Carroll and Villa defender Nathan Baker both needed lengthy treatment after a clash of heads when attacking the ball from N'Zogbia's corner.
Hammers on loan defender Emanuel Pogatetz was booked in first half injury-time for a foul on N'Zogbia.
West Ham dominated the early stages of the second period possession-wise and appealed in vain for a penalty after a challenge by Vlaar on Carroll.
Villa defender Ciaran Clark made a crucial clearance from a Mohamed Diame ball into the danger area after Guzan had failed to make a clean punch on his attempted clearance.
N'Zogbia curled a shot just past the far post after being teed up by Benteke.
But Bent came to Villa's rescue when he cleared a low goal-bound shot from Carroll.
Baker was yellow carded for bringing down Joe Cole in full flight but after 74 minutes Villa were celebrating as they broke the deadlock through Benteke's 15th goal of the campaign.
Referee Mark Clattenburg awarded a penalty after Mark Noble brought down N'Zogbia.
Up stepped Benteke to send Jaaskelainen the wrong way with his spot-kick.
With 11 minutes left N'Zogbia doubled Villa's lead with a superb free-kick after Tomkins brought down Bent.
N'Zogbia curled the ball over the defensive wall and past Jaaskelainen for his first Premier League goal of the campaign.
Westwood unintentionally set up a tense finale when he headed the ball past Guzan from a Joe Cole cross.
Then in injury-time Guzan blocked a shot from Kevin Nolan and turned aside a Carlton Cole header as Villa survived by the skin of their teeth.