An overnight score of 130.20 leaves Great Britain in second place overall as they bid to improve on the bronze medal they won in Beijing in 2008.
Britain ended the day behind a relaxed and confident Germany team following an incident-packed cross-country that saw 15 of 74 riders eliminated.
And Kristina Cook in fifth, Mary King in sixth and Zara Phillips in 10th all have realistic hopes of challenging in the individual competition.
Cook, making her second Olympic appearance after two bronzes in Beijing, epitomised Team GB’s stunning performance on the afternoon with a fast and clean round to put herself into medal contention.
The 41-year-old was delighted to produce the goods aboard Miners Frolic and hopes her performance will stop the teasing from team-mate Phillips.
"The emotion almost boiled over as I have had all day to think about it,” said the 2009 European Champion.
“It was a tough course and the going was firm so I was worried about studs.
“I knew I would have to go fast round and I am not that keen on going fast, so I do it once a year.
"Zara (Phillips) has been giving me hell. She calls me granny because she likes to embarrass me because of my age, but I am clearly not a granny. I am hoping they all think I have done well."
And King, competing in her sixth Olympic Games, produced a similarly excellent round aboard Imperial Cavalier.
The double Olympic medallist, and oldest and most experienced member of the team, had to deal with a minor stoppage, but still managed a round with just 5.2 penalty points.
The 51-year-old was proud of her mount and her horse’s performance in dealing with the tough Greenwich Park course, which leaves her in individual medal contention for tomorrow.
“At the start he was difficult to turn, he is a very big horse and is not totally suited to this course,” she said.
“I knew the steering would be difficult and I was thrilled with our time.
"I went as quick as I could but he was nervous of the crowds. He did a good job, but I had to be careful around those first twisty turns. He could have got out of control and gone into the crowds.
"Nicola (Wilson) is a good friend and she was really helpful. Her advice was ringing in my ears.
"It was quite a nice place to be stopped before the big climb. It didn't make any difference. If anything it helped him get up the hill."
In front of members of the Royal family, Phillips also went penalty-free to put herself in the mix for the medals – and she was delighted with how well High Kingdom performed on the day.
“He was so honest – awesome,” said the Queen’s granddaughter.
“It was hard work but you just have to get on with it.
“He’s a very suitable horse but lost a front shoe so it was even harder for him but he stepped up to the plate.
“It was so loud, you couldn’t hear your stopwatch beeping.
“Mary has been here five times before. We all have to do our best and hope it makes a difference.”
Wilson, called into the team to replace Piggy French who was forced to withdraw earlier this month, played the role of pathfinder and got Team GB off to a near-perfect penalty-free start.
"What a fantastic horse (Opposition Buzz)” she said. “He felt as though all his birthdays and Christmases had come at once.
“I feel so privileged to ride here. He was plenty fit enough and still full of running at the end.
"The noise of the crowd was completely deafening. I couldn't even hear my watch beeping at the minute markers."
William Fox-Pitt, a team silver and bronze medallist in the previous two Games, couldn’t get round inside the required 10:03.00 minutes time, and suffered 9.2 penalty points to end the day placed 22nd in the individual event.
Germany's Ingrid Klimke and Sweden's Sara Algotsson Ostholt were in joint first in the individual rankings going into Tuesday's jumping phase, but the scores were so close it remained anyone's game.
Riders said it was a challenge to navigate the twisting and hilly course of 28 obstacles inspired by everything from classic children's book The Wind in the Willows to ancient Rome.
"The course is challenging because of this up and down and turn. Everything is coming just quick, quick, quick," Klimke said. Her horse, she said, was the key.
"He made it easy for me."
Only eight other riders made it over the 5.7 km course within the allotted time of 10 minutes and three seconds.
Algotsson Ostholt's clean showing and solid rides by her team mates put the Swedish team in third place overall. New Zealand's Mark Todd, who has said he is in London firmly intending to go home with a medal, was third individually.
Horseshoes loomed large in the story of Monday's cross-country.
Several horses shed shoes, which made the going even more slippery underfoot. Many riders said they used extra-large studs to improve traction after seeing how slick the footing was between the fences.
Two of the obstacles - one inspired by an ancient Greenwich Park bandstand and the other by the quintessentially English game of cricket - proved particularly thorny for some horses.
The bandstand, a combination of two jumps, proved the day's biggest bogeyman. Two horses fell, two riders came off, several refused at least once and Brazil's Serguei Fofanoff was knocked out of contention after his mount Barbara refused three times.
Australia dropped to sixth place from second following the weekend dressage phase after Sam Griffiths fell at the bandstand and Clayton Fredericks's horse, Bendigo, took a tumble at the same obstacle.
There were no serious injuries in Monday's cross-country, the riskiest discipline in equestrian.
Japan and Canada had a tough day, with three of five riders on each team knocked out by falls.