The victory, thanks to Steph Houghton's brilliantly-taken second minute goal, meant Britain finished top of the group having won all three matches without conceding a goal and will now face Canada in the quarter-finals at Coventry on Friday.
Brazil also qualified for the last eight and will play world champions Japan in their last eight match in Cardiff on the same evening.
"The atmosphere was electric. We got off to a great start but had to concentrate and do the job," said Powell whose players did a lap of honour at the end.
"But all I am concentrating on now is the quarter-final with Canada. That's the only focus, but we want this to go on as long as possible."
Britain, who are emerging as real medal contenders, took the lead 90 seconds into the game when Brazil failed to clear a corner and the ball eventually fell to Houghton, who showed some superb skill to turn the defender and score from an acute angle.
Left-back Houghton also scored in the 1-0 win against New Zealand in Britain's opening game and in the 3-0 win over Cameroon.
Her goal against Brazil brought 70,584 fans to their feet - a record crowd for a women's match in Britain, beating the old record of 53,000 which was set at a women's club match 92 years ago.
It was also only 6,000 shy of the Olympic record of 76,489 set when the United States beat China in the 1996 final.
The atmosphere in the stadium was totally different to the usual one at either an England international or Cup Final and was far more relaxed, with the crowd largely appreciating the skills of both teams in a very sporting, Olympian manner.
And there was plenty to be impressed with as Brazil came back looking for an equaliser and going close when Alex Scott was forced to head against her own post after pressure from Marta and Cristiane.
Britain though, were often quicker to the ball than Brazil and should have doubled their lead after 56 minutes when Francielle tripped Eni Aluko to concede a clear penalty.
But Kelly Smith's left-footed spot-kick was a poor one, lacking pace and accuracy and Brazil keeper Andreia scrambled it away down to her left.
Brazil coach Jorge Barcellos said: "Of course I am disappointed, but we lost a match, not the title or a medal. Now we have to face Japan, they are the world champions and we have to play much much better."
