The goal was a huge relief to Derby, who had lost all four of their previous outings.
A succession of squandered chances looked like costing the Rams dear as City, who had been reduced to ten men for the last 30 minutes, clung on.
The turning point of the game came five minutes after the break when City defender Jamie McCombe had a rush of blood to the head.
First he dragged down Rob Hulse and then, when the two squared up dramatically, collapsed to the ground despite not being touched by the Derby striker.
That earned him a yellow card and two minutes later he chopped Hulse down again as he threatened to break clear giving referee Mike Russell no option but to show him a second card.
Until then City, still seeking their first away win, had looked more than a match for a disjointed Derby side and should have been ahead at the break.
Two golden chances were squandered by striker Alvaro Saborio as City had the better of the first period.
With just two minutes gone he rose unmarked in the six-yard box only to see his header somehow scrambled clear.
Then just before the break, man of the match, Dutch Under-21 international Evander Sno, put him clean through on goal.
But with just Stephen Bywater to beat, Saborio froze on the ball allowing Shaun Barker to make a last-ditch saving tackle.
For Derby striker James Vaughan, on loan from Everton, should also have marked his home debut with a goal but fired wide from 15 yards just before the break.
But the second half belonged to Derby after McCombe's dismissal, but manager Nigel Clough will have been disappointed with his side's lack of guile and composure in front of goal.
The Rams turned back the clock when Paul Dickov and Lee Hendrie joined Robbie Savage on the field but both substitutes were guilty of glaring misses.
It took a moment of inspiration to settle the match and to the joy of 27,000 fans it was Teale who supplied it.