The last Western pair left in gold medal contention, Boe and Mogensen prevailed 17-21 21-18 22-20 in an 83-minute marathon of unrelenting tension to set up a mouthwatering gold medal decider with China's world champion pair of Cai Yun and Fu Haifeng.
The dramatic victory, sealed when Lee agonisingly misjudged a line call on match point, drew a standing ovation from the packed crowd at the 4,800-capacity Wembley Arena, which included Denmark's thrilled Crown Prince Frederik.
It also gave third seeds Boe and Mogensen hope of becoming only the second European Olympic champions since badminton became an Olympic sport at the 1992 Barcelona Games.
The only other gold medal not won by China, South Korea or Indonesia was clinched by Danish men's singles champion Poul-Erik Hoyer Larsen at the 1996 Atlanta Games.
"It is one of the best matches we have played under as much pressure as an Olympics," 32-year-old Boe, a four-time European champion, told reporters.
"We could actually play (the final) now if the Chinese wanted. We will play on pure adrenalin. (Fatigue) won't be a problem at all ... They can just bring it on, we'll be ready. Looking forward to it."
China's Cai and Fu will also head into the match with huge motivation, having lost the gold medal on their home court at the Beijing Games to Indonesia's Markis Kido and Hendra Setiawan.
In contrast to Boe and Mogensen's gruelling battle, the Chinese pair simply outclassed Malaysian pair Koo Kien Keat and Tan Boon Heong 21-9 21-19.
"We performed normally," said China's Fu, a response as no-nonsense as his military-style hair-cut.
"Four years ago we won silver, so we're so excited about the forthcoming match. We regret that we couldn't get gold (at Beijing). Four years on, we want to make up for that regret."
Tournament organisers have been determined to return the focus back to the sport after the disqualifications of eight women players for their part in a match-throwing scandal to secure more preferable positions in the knock-out rounds.
But the women's doubles bronze medal match between Russia and Canada was a reminder that four of the strongest pairs from China, South Korea and Indonesia had been kicked out of the tournament.
Russia's Valeria Sorokina and Nina Vislova, and Canadian pair Alex Bruce and Michele Li had been eliminated from the preliminary group rounds but were re-instated after the disqualifications.
The Russian pair, ranked 18th in the world, ended up trouncing the 27th-ranked Canadians 21-9 21-10.
"We were delighted we had the chance to continue in this tournament and we gave it 100 percent when we got our chance," Sorokina told reporters.
The final of the women's doubles will be contested by China's second-seeded pair Tian Qing and Zhao Yunlei and Japan's fourth seeds Mizuki Fujii and Reika Kakiiwa later on Saturday.
Indian eyes will be on Saina Nehwal's bid to win her country a maiden badminton medal in the bronze medal decider before an all-China final in the women's singles.