Staunton burst forward and played a one-two with substitute Dele Adebola before striking the ball in off the upright from over 20 yards out.
The importance of the game was clearly not lost on Coventry who looked nervous in the opening exchanges.
One early mix-up in particular between City's loanee Richard Duffy and Luke Steele saw an indirect free-kick from a tight angle awarded for a back-pass.
Adam Virgo, however, drove his effort from Leon Knight's pass straight into the side-netting.
The game flared up in the 36th minute when an entanglement between Michael Doyle and Leon Knight on the floor led to heated exchanges between both sides. Though it appeared punches were thrown, the referee chose only to book Doyle and Mark McCammon.
From the ensuing free-kick, Knight hit the wall and the ball fell to Virgo, who flicked it past Steele into the opposite bottom corner only to see his effort chalked off for offside.
Coventry took the upper-hand immediately after the break when an innocuous looking corner from Stephen Hughes was adjudged to have been handled by Guy Butters.
Gary McSheffrey, whose record from the penalty spot has been at best shaky this season, made no mistake as he blasted the ball straight down the middle to cue wild celebrations among the home support.
Brighton, however, took just 15 minutes to drag themselves back into the game. The warning signs had been there - Gary Hart reached Paul Reid's pass and lobbed the ball onto the roof of Steele's net.
Moments later, Hart found Virgo in space and he made his finish across Steele from the edge of the area look easy.
Coventry piled the pressure on and ended the game with four strikers on the field - substitute Trevor Benjamin nearly had the best first touch of all time when his overhead kick forced a save from Alan Blayney, but Staunton's late intervention sealed the points for the Midlanders.
The importance of the game was clearly not lost on Coventry who looked nervous in the opening exchanges.
One early mix-up in particular between City's loanee Richard Duffy and Luke Steele saw an indirect free-kick from a tight angle awarded for a back-pass.
Adam Virgo, however, drove his effort from Leon Knight's pass straight into the side-netting.
The game flared up in the 36th minute when an entanglement between Michael Doyle and Leon Knight on the floor led to heated exchanges between both sides. Though it appeared punches were thrown, the referee chose only to book Doyle and Mark McCammon.
From the ensuing free-kick, Knight hit the wall and the ball fell to Virgo, who flicked it past Steele into the opposite bottom corner only to see his effort chalked off for offside.
Coventry took the upper-hand immediately after the break when an innocuous looking corner from Stephen Hughes was adjudged to have been handled by Guy Butters.
Gary McSheffrey, whose record from the penalty spot has been at best shaky this season, made no mistake as he blasted the ball straight down the middle to cue wild celebrations among the home support.
Brighton, however, took just 15 minutes to drag themselves back into the game. The warning signs had been there - Gary Hart reached Paul Reid's pass and lobbed the ball onto the roof of Steele's net.
Moments later, Hart found Virgo in space and he made his finish across Steele from the edge of the area look easy.
Coventry piled the pressure on and ended the game with four strikers on the field - substitute Trevor Benjamin nearly had the best first touch of all time when his overhead kick forced a save from Alan Blayney, but Staunton's late intervention sealed the points for the Midlanders.