Steph Houghton added to her burgeoning reputation with a fine finish from a tight angle in the second minute, a third goal in three games for the Arsenal full-back.
Brazil did hit the woodwork but the hosts were the better side, visiting keeper Andreia making several good saves including from veteran forward Kelly Smith’s second-half penalty.
Hope Powell’s side now have an impressive record of three wins, five goals and none conceded ahead of the quarter-finals.
They will face Canada for a place in the semis, with a likely last-four clash against women’s powerhouse the USA, who face New Zealand, who snuck through as a best third-placed side from England's group.
Brazil play world champions Japan in a tough last-eight clash, with the winner of that tie facing either France or Sweden.
In front of a record crowd for a women's game in Britain (70,584) it was a keenly-contested match between teams with contrasting styles, with Britain's direct approach the more effective - they now have 31 attempts on target from their three group matches, the best in the tournament.
Brazil, as expected, played the prettier football, although they were limited to long-range efforts from front two Marta and Cristiane, most of which either flew well off target or straight at England keeper Karen Bardsley.
But they defended poorly at times, including in the second minute when they failed to clear their lines following an early GB corner: Karen Carney picked out Houghton, who rounded the keeper before sliding home a beautiful finish from an acute angle.
Early in the second half, another defensive howler was also punished, as Eniola Aluko - who had just missed a good opportunity - raced through a gap in the defence before being hauled down by Francielle.
The Brazil defender was fortunate to stay on the pitch, only booked for the cynical foul, and Smith - yet to score in these finals - missed from the spot, putting a weak penalty Andreia's left, easily kept out by the keeper.
Brazil sensed a comeback but they were unable to make much of an impact on a British defence superbly marshalled by Alex Scott and Casey Stoney, with Houghton showing the other side of her game with some timely challenges.
GB were hardly hanging on by the end, dictating the tempo and even hunting a third as Andreia saved well at the feet of Scotland's Kim Little.
Powell, who coaches all-but two of the squad with England's senior side, now has a 100 per cent record for Britain at the Olympics. And if they maintain this level of performance against Canada in Coventry, a mouth-watering semi-final with the US beckons.
"The atmosphere was electric, we got off to a great start and had to concentrate to finish the job against a very good Brazil side," Powell said.
At least Powell started the match determined to win it unlike Japan coach Norio Sasaki who said after qualifying with a 0-0 draw with South Africa in Cardiff that he instructed his side not to push for a winner at the Millennium Stadium.
The result saw Japan finish second behind Sweden in Group F, meaning they remain in Cardiff for their quarter-final against Brazil while Sweden, who won the group, play Group G runners-up France at Hampden Park.
Sasaki said the result was ideal for his squad.
"We wanted to stay here for the next match. It was important not to move to Glasgow but to stay here and prepare for it.
"Before the match I did not tell the players to draw the game, but if we had a situation during the game - we might have some kind of an instruction to draw the game and it happened like that.
"It was a different way of playing compared to our usual game but I think the players were at the same stage and understood my instructions well."
An official from FIFA said no action would be taken because there was no collusion between the sides to engineer a result.
Canada recovered from two goals down with a double from Melissa Tancredi to draw 2-2 with Sweden at St James' Park, Newcastle, the result meaning they were one of the two best third-placed finishers and they now play Britain at Coventry.
New Zealand, who lost their opening two games, recovered to beat Cameroon 3-1 and claim the other best third-place berth to set up a quarter-final with the US in Newcastle on Friday.
The US, meanwhile, clinched top spot in Group G after Abby Wambach's 25th minute goal gave them a 1-0 win over North Korea and a 100 per cent record of their own at Old Trafford.
The three-time gold medal winners are on nine points, having also beaten France and Colombia, and victory at Manchester United's stadium was far more comfortable than the final scoreline suggests.
Pia Sundhage's team, who had already clinched a place in the last eight, were rarely caused problems by a hard-working but tactically negative North Korea team.
The Koreans, who finished third in Group G with three points, must wait to see if they will progress as one of the two third-placed teams with the best record.
The US went close to opening the scoring in the fifth minute when Wambach and Carli Lloyd linked up well to put in Alex Morgan whose low shot was tipped around the post by North Korea keeper O Chang-ran.
The influential Wambach continued to stretch the North Korean defence and in the 15th minute she burst down the left flank and slipped the ball inside to Morgan, who turned sharply and fired a low shot against the post.
It was no surprise when that combination gave the Americans the advantage, Morgan bringing down a long ball into the area from Lloyd, turning well again and sliding a smart pass to Wambach who made no mistake.
From then on it was 'game management' mode from the US while North Korea, who needed a draw to be sure of reaching the quarter-finals, frantically sought a way back into the game without ever throwing many players forward.
The North Koreans were reduced to 10 players in the 81st minute when Choe Mi Gyong was sent off for a second yellow card following a reckless challenge on Lauren Cheney.
The nearest North Korea came to getting a crucial equaliser was four minutes from the end of regulation time when Choe Un-Ju's long-range effort dipped just over Hope Solo's bar.